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ARE YOU GETTING WHAT YOU PAY FOR?: AN ANALYSIS OF THE EDUCATION PRODUCTION FUNCTION IN SOUTH CAROLINA BY ERIN LAPEYROLERIE A Thesis Submitted to the Division of Social Sciences New College of Florida in partial fulfillment of the requireme nts for the degree Bachelor of Arts Under the sponsorship of Richard Coe, Ph.D and Tarron Khemraj, Ph.D Sarasota, Florida May 2013
! "" Acknowledgements I would like to thank Dr. Richard Coe who took me on as a thesis student half way through the year. Dr. Coe has played a significant role in introducing me to how economics can be applied to my passion of social justice. Dr. Coe's Distributive Justice course was one of the most influential courses in shaping my academic career. I would like to thank Dr Tarron Khemraj for co sponsoring this thesis and helping me understand the econometrics needed for this thesis. I would like to thank Dr. Sarah Hernandez for working closely with me as I developed the base of my thesis. She assisted me in the first seme ster as if I was her thesis student, and that got me off to a great start! I would like to thank Dr. Duff Cooper for the hours he spent working with me to clean my data set. Also, he taught me core skills in using SAS. I would like to thank Dr. Tracy Co llins for helping me narrow down my thesis topic. I would also like to thank her for helping me with future plans! I would like to thank Kortney Lapeyrolerie for being my best friend and sister since 1991. I am so grateful that I was able to spend my unde rgraduate years with her. I would like to thank Minorateam for being my New College family. Minorateam has consistently been by my side, and I believe they have all played a role in my ability to view the world, and my place in the world, critically. My friendships with these women embody perfection and sisterhood. I would like to thank Heather Barnes for encouraging me throughout this process. Heather always brings me joy, even after the longest of days and I am beyond lucky to have them in my life. I would like to thank Tristan Zucker for discussing concepts with me, even though he is all the way in Boston!! I would like to thank the South Carolina Department of Education for clarifying any questions I had throughout my thesis process. I would like to thank Aaron Baker for his support throughout this year. He has been a fantastic supervisor this year and has worked to help me build a plan for the years that are to follow my time at New College. I would like to thank my loving and supportive parents, Daryl and Jacqueline Lapeyrolerie, for investing so much in my education. They believe strongly in the power of education, and hopefully my future yields positive returns to their investments.
! """ Table of Contents Introduction .. .. 1 Importance of Education..... 1 The Education Producti on Function.... 3 Focus of this Study.. 6 Chap ter 1: Literature Review ............................... 9 Relevant Historic Literature: The Coleman Report........ 11 Expenditure and Studen t Achievement...... 15 Teachers and Studen t Achievement... 18 Classroom Characteristics and Student Achievement 21 Chapter 2: Education in the United States .. ... 23 Financing the Public Ed ucation System..... 23 Reforms .. ... 25 Testing and Eight h Grade....... 27 De Facto Segre gation..... 29 Gender Inequa lities.. .. ..... 31 South Carolina and Pub lic Education. 32 Financ ing.... 35 Chapter 3: Methodology. 41 Data 41 Sample Size and Characte ristics... .. .. .. 42 Education Production Fu n ction Model....... 45 Data Transfor mations..... 47 Data Limita tions..... 48 Diagnost ics. 49 Chapter 4: Results .... .. 50 Englis h Language Arts... 5 2 Mathematics .. .. ... 54 Other Estim ates.. 55 More than 50%....................................................................... ................ 57 Overall Signifi cance... 59 Chapter 5: Conclusi on..... ... 62 Expenditure and Studen t Achievement.. 63 Teachers and Student Achievement... 64 Classroom Characteristics and Student Achievement.... 65 Student Body Demographics an d Student Achievement .. .... 66 Policy Implic ations..... 67 Future S tudies. 69 Appendix A: Correlation Tables ... 71 Appendix B: Descriptive Statistics. 73 Appendix C: Diagnostic Tests ............... ......... ............................ 77 Works Cited .... ... 83
! "# List of Tables and Figures Table 1.1 PASS Score C ategoreies.. .. 42 Table 1.2 Main Analysis Dependent Variables Mean, Minimum, an d Maximum.. .. 43 Table 1.3 Schools in which more than 50% of Test Takers are Eligible for FRL Dependent Variables Mean, Minimu m, and Maximum.. .. .. 43 Table 2.1 Model 1 R esults: English Language Arts.. ..... ................... ........ 50 Table 2.2 Model 2 Re sults: Mathe matics ....... .. 51 Table 2.3 Model 3 Results: Science... ... 52 Table 2.4 Model 4 Results: Soc ial Studies.. .. ......... ... .. 53 Table 2.5 Model 5 Results : Writing...... 54 Table 2.6 Model 1 Result s: English Language Arts Where more than 50% are eligible for FRL....... ........................... 55 Table 2.7 Model 2 Results: Mathematics Where more than 50% are eligible for FRL.............. 56 Table 2.8 Model 3 Results: Science Where more than 50% are eligib le for FRL...... 57 Table 2.9 Model 4 Results: Social Studies Where more than 50% are eligibl e for FRL ..... 58 Table 2.10 Model 5 Results: Writing Where more than 50% are eligi ble for FRL ..... 59 Table 2 .11 Significant Parameter Estimates For M ain Analysis. .. 60 Table 2.12 Significant Parameter Estimates For Schools in Which More than 50% of the Test Takers are Eligible for FRL.. 61 Table A.1 English Independent and D ependent Variable Corre lation Table...... 71 Table A.2 Mathematics Independent and Dependent Variable Corre lation Table...... 72 Table B1 Main Analysis Independent Variable Mean, Minimum, and Maximum... 73 Table B2 Schools in which more than 50% of English Languages Arts Test Takers Are Eligible for FRL Independent Variables Mean, Minim um, and Maximum...... 74 Table B3 Schools in which more than 50% of Math Test Takers Are Eligible for FRL Independent Variables Mean, Minimum, and Maximum.. ... 74 Table B4 Schools in which more than 50% of Science Test Takers Are Eligible for FRL Independent Variables Mean Minimum, and Maximum .. 75 Table B5 Schools in which more than 50% of Social Studies Test Takers A re Eligible for FRL Independent Variables Mean, Minim um, and Maximum...... 75
! # List of Tables and Figures Continued Table B6 Schools in which more than 50% of Writing Test Takers Are Eligible for FRL Independent Variables Mean, Minim um, and Maximum ... .... ............ 76 Table C1 White Test Results 77 Figure C1 Model 1 English Language Arts Heterosk edasticity. 77 Figure C2 Model 2 Math Heterosk edasticity............ 78 Figure C3 Model 3 Science Heteroskedasticity78 Figure C4 Model 4 Social Studies Heterosked asticity.. 79 Figure C5 Model 5 Writing Heteroskeda sticity 79 Table C2 Model 1 English Language Arts Multico llinearity.. .. .. 80 Table C3 Model 2 Math Multicollinearity ... 80 Table C4 Model 3 Science Multicollinear ity..... 81 Table C5 Model 4 Social Studies Multicoll inearity... ... .. 81 Table C6 Model 5 Writing Multicolli nea rity.... .. 82
! #" ARE YOU GETTING WHAT YOU PAY FOR?: AN ANALYSIS OF THE EDUCATION PRODUCTION FUNCTION IN SOUTH CAROLINA Erin Lapeyrolerie New College of Florida, 2013 ABSTRACT Ideally, students would attain a quality educ ation from the United States public education system. However, the exact relationship between various education inputs and student achievement is still uncertain. Using the 2011 2012 Palmetto Assessment of State Standards (PASS) for the 8 th grade, this stu dy is designed to analyze the education production function in South Carolina at the school level. Five subject tests were analyzed in this education production function, which measured the relationship between the percent of students who met or exceeded s tate standards and school inputs, while controlling for student demographics. The results of this study suggest that school resources do not matter; there is not a statistically significant relationship for a single school resource across all five subject tests. The majority of the school inputs do not have a statistically significant parameter estimate. However, the suggestion that school resources do not matter is challenged in suggesting that the results suggest that the public education system is not us ing these resources effectively. This final suggestion implies that a structural change is needed to improve the education system. Dr. Richard Coe Dr. Tarron Khemraj Division of Social Sciences Division of Social Sciences
! $ Introduction Importance of Education Public education is recognized as an important resource in the United States. However, there are questions as to which inputs are positively related to student achievement, and whether or not these inputs are distributed and utilized in an e quitable and efficient manner. The main reasons public education is a focus of concern can be analyzed on both the personal level and on the public level. The level of education attained is related to an individual's expected lifetime income (Checchi 7). Two theories that illustrate the significance of education in the United States for an individual are the human capital theory and the signaling theory. A third concept that relates the impact of education to the wellbeing of the individual is the relation ship between intergenerational immobility and education. "Schooling is perceived as an important determinant of individual produ ctivity and earnings" (Hanushek, "School Resources" 43). The human capital theory relates education to personal investment, sug gesting that an investment in education will impro ve the level of income (Checchi 19). Ideally, income would be directly related to the level of productivity and the marginal cost of educating the individual would equal the marginal benefit (13). So, educa tion would improve an individual's level of productivity, improving the level of income the individual earns (20). The signaling theory suggests that an individual's level of education allows firms to assume information about an individual's level of prod uctivity (Checchi
! % 176). The individual's level of attained education signals the "private information" of the individual, specifically their productivity As previously mentioned, in an ideal situation, the marginal product ivity of the worker would be used to determine the worker's income or wage. Both the human capital theory and signaling theory are flawed. The human capital theory is not fully supported, because there is limited evidence illustrating a relationship between an individual's level of educa tion and their level of productivity (Checchi 12). The signaling theory is challenged because it depends on there not being "barriers in accessing education" (13). However, barriers, such as financial constraints, impede access to education. Intergenerati onal immobility is expected to decrease as a result of access to education. "Limited access to education is proved to contribute to income inequality persistence over generations" (Checchi 11). For example, an educated parent increases the likelihood of t he child being educated (215). One reason for this may be that educated parents have more access to resources for their children. For example, they may have greater access to learning what schools are of a higher quality (216). A cause of intergenerational immobility may be related to the parent's income, impacting the amount of money a parent has to invest in their child's education. Less affluent parents can invest less money in their child's education. Ideally, public education will create equal opportun ity to a ttain education and to increase the social mobility of disadvantaged people, which would reduce the intergenerational immobility. The public investment in education is a factor that is considered to improve "structural mobility" (Checchi 217).
! & Th e public is faced with both benefits and costs of public education. For example, "while not often subjected to much analysis, schooling is assumed to generate various externalities" (Hanushek, "School Resources" 43). Thus, if public education fulfills its expectations, it is expecte d to positively influence various important aspects of society such as the economy. On the other side, public education is an expensive resource (Burtless 1). The portion of the GDP invested in public education illustrates the e xpense; i n 2009, 5.4% of the GDP was invested in education ("World Factbook"). The Education Production Function In an attempt to identify a way to find the relationship between education inputs and student achievement, scholars have produced an educatio n production function. The education production function is defined as a production function that measures the relationship between school outputs and the inputs that affect education (Bowles, "Towards" 12). One reason the development of the education prod uction function is important is because the results could assist in the development of education policy. As previously mentioned, education is considered to have the capacity to improve productivity, increase an individual's level of income, and reduce int ergenerational immobility. Public education increases this possibility by reducing the barriers to education access. However, t here are trade offs concerning equity and efficiency (Checchi 12). Focusing on e quity would improve the access to education for a ll individuals. However, if the education system was designed to fo cus on
! efficiency, there may be greater investment in more capable students A strong education system would find a balance between equity and efficiency. In explaining why research is cond ucted on student achievement, Hanushek links the concern to the concept that schools can increase the productivity of people who will later enter the labor market, increase their capacity to exercise democratic rights, and improve their consumer decisions ( "The Economics" 1151). Studying the education production function does have challenges. One challenge confronting the quality of the previous research results is the quality of the data used. Challenges include the quality of data when aggregated and the issue of missing data. Data utilized in education production function studies are frequently collected for other purposes (Hanushek, "The Failure" F74). An example of a dependent variable in the education production function is student performance. Stude nt performance is typically measured through test scores, dropout rates, performance in college, and income (Hanushek, "School Resources" 60). Test scores are available measures of achievement and are "valued in and of themselves" (Hanushek, "The Failure" 1154). Test scores influence a number of academic decisions, including whether or not students can continue with their education or graduate. Independent variables typically studied in the education production function can b e categorized into school inpu ts and student demographics School inputs include variables such as expenditure, teacher quality, and classroom characteristics. The parameter estimates of school inputs in Hanushek's meta study illustrates that the direction of parameter estimates are in consistent ("Assessing" 144). This study also
! ( illustrates that the majority of the estimates are statistically insignificant. Fifteen percent of the 277 teacher student estimates are positive and statistically significant. Nine percent of the 171 teacher e ducation estimates are positive and statistically significant. Twenty nine percent of the 207 teacher experience estimates are positive and statistically significant. Twenty percent of the 119 teacher salary estimates are positive and statistically signifi cant. Twenty seven percent of the 163 expenditure per student estimates are positive and statistically significant. In discussing results that illustrate the lack of a relationship between school resources and academic achievement, Hanushek illuminates the fact that the results "do not say that school resources could not be effective in raising student achievement; they say only that there is little reason to expect improved achievement from added resources in schools as currently organized and run" ("Sc hool Resources" 57). Some studies present a positive relationship between school resources and student achievement. In Unequal Childhoods Annette Lareau presents two schools: Lower Richmond (an inner city school) and Swan (a suburban school) (15). The res ources at Swan are significantly greater, from teacher resources, like a copy machine, to student opportunities, like fieldtrips (21). There is also a contrast between the achievement levels of the students in these two schools; while the students at Swan read at or above grade level, 1/3 of the fourth graders at Lower Richmond are at least two years behind grade level (18). Student demographic variables considered in the education production function include race, class, and gender. Hanushek highlights a n umber of aspects that may negatively affect student achievement, including poverty ( "School
! ) Resources" 50). For example, between the years of 2003 and 2011, 4 th and 8 th grade students who were not eligible for free or reduced price lunch (FRL) received hig her scores than students who were qualified for FRL (Kober and Usher 45). Previous research suggests "school poverty concentration affects students' opp ortunities to learn" (Archibald 36). In contrast to authors who believe that the schools help promote opportunity, Bowles and Gintis illustrate the "reproduction function of education" (124). The reproduction function of education suggests that there is an inter section of education and the capitalist nature of the United States. "They [schools] create and reinforce patterns of social class, racial and sexual identification among students which allow them to relate properly' to their eventual standing in the hierarchy of authority and status in the production process" (Bowles and Gintis 11). Thus, it is br ought into question whether or not social structures based on race, class, and gender can be influenced by the education system (25). Focus of this Study This study is designed to analyze the education production function in South Carolina. I chose Sout h Carolina because I was raised in the South Carolina education system. I saw education achievement disparities on the surface while I was a student in the system, thus I wanted to explore the production function more thoroughly. I chose PASS because I wan ted to choose a standardized test that was not targeted towards students probably planning on attending college. I wanted to maximize the diversity of the student populations of the schools being studied.
! The data for this study includes the percent of 8th grade students per school who met or exceeded state standards for the Palmetto Assessment of State Standards (PASS) exam for the academic year of 2011 2012, a breakdown of the schools' test taker demogra phic by percent and the average expenditure per stu dent. Data for other expenditure, teacher, and classroom characteristics are included, as well. PASS is a state standardized test used to measure the levels of educational attainment for students in grades three through eight ("Palmetto Assessment of State Standards (PASS) Grades 3 8"). PASS is made up of five tests: English/Language Arts, Mathematics, Science, Social Studies and Writing These tests are multiple choice tests with the exception of the extended response item" in the W riting section. PASS h as three performance levels: exemplary, met, and not met. These all relate to the fact as to whether or not the student exceeded, met, or did not meet the state's grade level standards. Thus, for this study, the level of educational attainment will be meas ured by the percent of students who met or exceeded state standards. Using a multiple regression model and a cross sectional data set, this study is designed to measure the relationship between education achievement and expenditure per student, teacher ch aracteristics, and classroom characteristics, controlling for the demographics of the student population being served. Thus the research question is whether or not school inputs positively contribute to student achievement, independent of student demograp hics in the South Carolina public education system In this study, the majority of school inputs are found to be insignificant in all of the schools and in the schools in which more than 50% of the test takers are eligible for FRL In analyzing the relat ionship between school inputs and student
! + achievement there a re a few variables that are significant T here is not a single school input variable that is statistically significant for all five subject tests. Thus, there is not a direct statistically signi ficant relationship between the levels of various school inputs and student achievement across the different subject tests.
! Chapter 1: Literature Review Over the past few decades, there have been multiple studies that are designed to question what educ ation inputs yield higher returns to education, which can be measured through student achievement levels This section will review some of the literature addressing this question. In previous studies, the returns to public education inputs have been measur ed in multiple ways and are frequently, but not consistently, found to be insufficient. Various studies analyzing the education production function have conflicting results. Some of the contradictions are dependent on varying models or methodology. For ex ample, Hanushek completed a study summarizing hundreds of parameter estimates for school resources ( "Assessing" 14 2). Some measures of education inputs can be grouped into three categories: "real resources of the classroom," which included education levels of teachers, experience of teachers, teacher student ratios; "financial aggregates of resources," which included expenditure per student and teacher salary; and "measures of other resources in schools," which included characteristics of teachers, school f acilities, and measures of inputs related to the administration (143). In general, 15% of the estimated effects of teacher student ratio on student performance were positively and statistically significant while 13% were negatively and statistically signif icant (144). For teachers' education, 9% were positively statistically significant and 4% were negatively statistically significant. For teachers' experience, 29% were positively and statistically significant while 5% were
! $! negatively statistically signific ant. For expenditure per pupil, 27% of the estimates were positively significant while 7% were negatively significant. The results were also presented with respect to various levels of aggregation to illustrate the e ffects of aggregation on the results of a study, as "aggregation of explanatory variables reduces the precision of any estimates but does not lead to biased estimates" (145). For example, measuring the effect of expenditure per student on student performance at the classroom level there is 0% positive and significant estimates and 0% negative and statistically significant (145). At the school level, 17% of the estimates are positive and statistically significant and 7% are negative and statistically significant. At the district level, 28% of th e estimates are positive and statistically significant and 9% are negative and statistically significant. At the county level, 0% of the estimates are positive and significant estimates and 0% negative and statistically significant. At the state level, 64% of the estimates are positive and statistically significant and 4% are negative and statistically significant. The results are also presented in respect to whether the samples of the studies were derived from one or multiple states (147 8). While the resu lts are presented in multiple ways, the basic conclusion is "there is no strong or consistent relationship between school resources and student performance" (148). Hanushek is clear to highlight that these findings d o not mean "schools and teachers are the same" (148). Rather, it suggests that the inputs being studied and manipulated in policy do not measure the differences. In referencing his 1986 review of previous studies in a later article, Hanushek states that there is a lack of evidence illustrating t he relationship between class size
! $$ and student achievement and a lack of evidence illustrating that the degree attained by the teacher influences student achievement ( "Educational" 41). There is little evidence illustrating the relationship between the exp erience of the teacher and student achievement. However, Hanushek clearly states that these results do not belittle the influence of teachers on student achievement. Instead, he challenges the sufficiency of standard measures of quality; "The best teachers are not the highest paidthe good schools are not the ones that spend the mostthere is no consistency across schools and experiences" (41). Relevant Historic Literature: The Coleman Report The Civil Rights Act of 1964 requested a report with which the r esults of a survey would measure the distribution of educational opportunities with respects to the diverse student population in the United States (Howe iii). This report is the Equality of Educational Opportunity better known as the Coleman Report The Coleman Report is described as being "both the best known and the most controversial" and "seriously flawed" (Hanushek "The Economics" 1150). The results suggested that student qualities, such as familial characteristics and peer characteristics, influen ced student performance more than the characteristics of the schools. Hanushek challenges the results of the Coleman Report in reviewing a number of other studies, stating that school characteristics influence student performance when the characteristics o f the schools are measured correctly ( "The Economics" 1159). While a source of great controversy, the Coleman Report is also noted as an important step towards researching the role of school inputs and student
! $% background on student achievement. The survey was developed with intentions to collect information concerning the racial and ethnic segregation in public schools, the equality of the distribution of educational opportunities, the level of student learning, and the relationship between "the kinds of sc hools" and student achievement (Howe iii iv). While the Coleman Report consists of survey results that were derived at an earlier point in the United States history, a historical presentation of the analyses of the returns to school inputs and the treatme nt and achievement of a diverse student body population can assist in developing a general picture of the effectiveness of public schools in the United States. D ifferences provided by history will influence the condition of the education system at the tim e of the study For example, this report illustrates a historic disparity in the distribution of education resources in finding that "nationally, Negro pupils have few of some of the facilities that seem most related to academic achievement" (Coleman et al 9). A h istorical comprehension of the quality and distribution of American public education is necessary in attempting to identify the inputs that effectively improve the education process. The Coleman Report opens by highlighting the significance of se gregation in American schools (Coleman et al. 3). The principal way in which the school environments of Negroes and whites differ is in the composition of their student bodies, and it turns out that the composition of the student bodies has a strong relat ionship to the achievement of Negro and other minority pupils" (22). In the
! $& South, most black and white students attended schools that were completely racially segregated. The second subject addressed are school characteristics, which is described as an e xpansive subject that can be inclusive of all the various aspects of the school, such as the facilities and teachers ( Coleman et al. 8). "One must picture the child whose school has every conceivable facility that there is believed to enhance the educatio nal process And one must picture the child in a dismal tenement area who may come hungry to an ancient dirty building" (8). On a national level, the survey found that black primary and secondary s tudents had a higher student teacher ratio than white stud ents (9). The same held true for other minority students, with the exception of American Indian secondary school students. In comparing median test scores of students, the median scores for black students were lower than those for other students. In gene ral, minority students had lower average test scores than white students ( Coleman et al. 20). After controlling for socioeconomic differences, this report states, "it appears that differences between schools account for only a small fraction of differences in pupil achievement" (22). However, the school and teacher characteristics have a greater influence on minority student achievement. "The inference might then be made that improving the school of a minority pupil may increase his achievement more than wo uld improving the school of a white child increase his" (22). Characteristics of classmates will also influence the achievement of minority students, with the exception of Asian students, more than white students.
! $' Bolwes and Levin review the Coleman Report and illuminate some of its flaws. They first illustrate the flaws in the data that was used in this study. There are biases that result from an under representation of schools in big cities and the treatment of the sizable number of "nonresponses" on the survey that was distributed to the schools ( "The Determinants" 6). "These nonresponses were simply given the arithmetic mean of the responses, an ingenuous treatment which has probably created sever e measurement errors in the data" (6 7). The responses to the survey included many blanks for aspects that would measure students' background, such as measures of parents' education (7). In addition, the blank responses were not randomly distributed. Studies that attempt to find the relationship between school i nputs and achievement are influenced by how they measur e the inputs. Bowles and Levin challenge the sufficiency of the measurement of inputs in the Coleman Report ( "The Determinants" 8). For example, the data of instructional expenditure per student analy zed in the study was collected at the district level rather than the school level, ignoring v ariations within di stricts (8). This causes "an understatement of the effect of per pupil expenditure" (9). In discussing "control on student background" for the Coleman Report Bowles and Levin bring into question the overlap of race and class (22). "In general, Negroes who are attending predominantly white schools are representatives of a considerably higher socioeconomic class than are students in all, or largel y Negro schools" (22). Thus, the general racial makeup of the student body may signal the general socioeconomic makeup of the student body.
! $( In a separate article, Bowles and Levin challenge the conclusions, address ing the problem of multicollinearity in th e variables used in the Coleman Report ("More") Bowles and Levin evaluate the independent variables through two tests and find a level of multicollinearity that would cause a smaller relationship between academic achievement and school resources (395). B owles and Levin ran a regression in attempt to find "more significant estimates" than those presented in the Coleman Report in order to illustrate that the survey doe s not present strong evidence for minimizing the relationship between schooling inputs and academic achievement ( "More" 398 399). In the process of doing so, they chose not to test the variables that previously had insignificant coefficients to reduce multicollinearity. The new estimates suggest that teachers' salaries, teacher quality, and sch ool facilities, as measured by the presence of science laboratories, are significantly related to academic achievement, as measured by the verbal scores of black students (399). When measuring for white students, the level of significance was lower. Expen diture and Student Achievement Research illustrating the relationship between education expenditure and student achievement is inconsistent Hanushek states that there is no strong or consistent relationship between school resources and student performance ( "Assessing" 148 ). Out of 163 previous estimates for expenditure per student, 27% are statistically significant and positive and 7% are statistically significant and negative (147). Eighty nine of these estimates were based on dat a from an individual
! $) state, rather than across multiple states, and 20% were statistically significant and positive while 11% were statistically significant and negative. Some studies have illustrated a positive relationship between expenditure per pupil and stu dent achievement (Archibald; Ram; Wenglinksy). Archibald analyzes the effects of teacher, student, and school specific variables in attempt to find what impacts student achievement in reading and math. Minority status, low economic class status, and elig ibility for special education are negatively related to student achievement (33). Using school level data, the results illustrate a statistically significant, positive relationship between expenditure per student and student achievement (34). Ram stu died the relationship between spending per student and student achievement in the United States, focusing on math and verbal SAT achievement (170). The results illustrate a positive and significant relationship between math test scores and expenditure per student (173). The relationship between verbal test scores and expenditure per student is positive and statistically insignificant. Overall, the relationship for student achievement, as measured by SAT scores, and expenditure per student is significantly positive. Wenglinksy highlights the effects of expenditure per student on student achievement through the analysis of the utilization of the expenditures. The expenditures are categorized; the categories include expenditure for instruction and expenditure for school district administration (221). According to this study, increasing expenditure per student in these sectors reduces the student teacher ratio (229). The reduced student teacher ratio improves the environment of the school.
! $* There is a positive r elationship between student achievement in math and school environment. Through analyzing specific use of expenditure per pupil, the results illustrate that expenditure per student is positively related to student achievement. These results were statistica lly significant. Some studies present results illustrating that expenditure does not relate to test scores (Marlow; Okpala, Okpala, and Smith). Marlow explores the issue of competition in maximizing the returns to education by analyzing California school s. Marlow argues that education institutions would increase its achievement levels if there were a greater sense of competition. For example, the increase in expenditure may be used on factors that do not relate to student achievement in a public education system (91). In the study, Marlow uses data for the academic year of 1993 94, measuring the achievement levels for students in the fourth, eighth, and tenth grade. In reference to the regressions that utilized expenditure per pupil, the equations utilizin g fourth, eighth, and tenth grade math achievement as a dependent variable found that the percentage of black and Hispanic students were significantly and negatively related to math achievement (99 100). In general, this study found that there is not an ap parent positive relationship between education expenditure and students' academic achievement (102). The general results also suggest that higher market power increases the level of education spending and decreases the level of academic achievement (103 4) Okpala, Okpala, and Smi th studied the influence of parent involvement, family background, and expenditure on fourth grade math achievement for students attending school in a North Carolina county (112). These influences are being
! $+ measured to determine the factors that constitute a quality schooldefined as one that produces the maximum number of students who achieve at the expected mastery level" (111). The variables include parental involvement, as measured by volunteer hours, and family socioeconomic class, as measured whether or not the student receives free or reduced price lunch (112). The expenditure per student variable was measuring spending on instructional supplies (113). The relationship between expenditure per student and student achievement and the relationship between parent involvement and student achievement are not found to be statistically significant (114). The relationship between socioeconomic class and student achievement is negative (115). Teachers and Student Achievement Another s et of variables to consider in the education production function illustrates the relationship between teachers and student achievement. The role of teachers in the education production function is measured through a number of variables. One way to measure teacher quality is through the "val ue added method. Another way to measure teacher quality is through various variables, such as teachers' credentials, the teachers' attendance rate, and the professional development the teacher has attained. In general, there appears to be concern that teacher quality is difficult to measure. However, even if it is difficult to measure teacher quality, it is still accepted that teacher quality influences student achievement. "Good teachers certainly exist; it is just tha t good teachers are not different from bad in terms of class sizes, salaries, education, and the like" (Hanushek, "School Resources" 59).
! $, Chetty, Friedman, and Rockoloff conducted a study to find the influence of teachers through a "value added" approach. The school grade data covers years 4 8 (3). Using the value added as a measure for teacher quality, "VA teachers" are positively and significantly related to many aspects of a students' future (4). A student having a higher VA teacher for one grade is sign ificantly more likely to attend college (36). The quality of the teacher is also positively and significantly related to the quality of the college the student attends (37 8). Other factors significantly influenced by VA teachers are the future earnings o f students, the age the student has a child, the quality of where the student lives as an adult, and the rate of savings for retirement (4). Teacher quality influences females more in this study. In general, this study finds teacher quality to be a signifi cant factor in the students' lives. Hanushek analyzed results from a set of studies that used the value added approach. Out of 33 value added teacher education estimate zero were positive and statistically significant (" Assessing 59). However, out of th e 36 studies measuring teacher experience, 39 were positive and statistically significant. Research has illustrated a positive relationship between teacher experience and student achievement (C lotfelter, Ladd, and Vigdor; Harris and Sass ). According to a N orth Carolina study analyzing the relationship between third, fourth, and fifth grade math and reading achievement and t he credentials of the teachers, some teacher credentials positively affect student achievement (Clotfelter, Ladd, and Vigdor 673). Teac hers' credentials include variables such as their experience teaching, graduate degrees, and teacher test scores. Some teacher credentials are positively related to student achievement, and, in this particular study, the influences are greater on math
! %! achi evement (681). The years of experience teaching and teacher test scores are positively related to the student achievement (675). Graduate degrees, without specifying the level of the graduate degree, do not have a statistically significant effect on studen t achievement (677, 679). Archibald found mixed results for the relationship between teacher quality and student achievement (34). Using c lass level data, there is a positive relationship between student achievement and the quality of the teacher, as meas ured by an evaluation system. However, there is a negative, insignificant relationship between student achievement and the teacher's attainment of a master's degree or years of experience. Harris and Sass measure the relationship between teacher quality an d training and the level of student achievement. The general findings were that productivity of teachers that work in elementary and middle schools is positively related to early experience, as opposed to formal training (810). For example, advanced degree s are not correlated with elementary school teacher productivity (811). Advanced degrees, however, are related to achievement for middle school math (810). It is suggested that formal training may not have a positive significant relationship to students' a cademic achievement levels because formal training is "too standardized," while "teacher productivity is context specific" (811). Huffman, Thomas, and Lawrenz analyze the effects of teachers on student achievement through professional development (379). T he focus of this study is the achievement in eighth grade math and science (380). Multiple forms of professional development were taken into consideration, such as curriculum development and
! %$ immersion (382). The results did not illustrate a statistically significant relationship between math or science student achievement and the various forms of professional development, with the exception of a negative relationship between math achievement and curriculum development (382). Miller, Murname and Willett ana lyze the relationship between teacher attendance and student achievement (181). There is a significant negative relationship between teacher absence and student achievement (192). This relationship is negative for both math and English language arts, but t he estimates for math have a greater magnitude. Planned absences have less of an influence on student achievement than unplanned absences (193). Classroom Characteristics and Student Achievement Other school qualities to consider are the student teacher ratio and the percent of prime instructional time. The student teacher ratio is a measure of class size. Some studies illustrate a favorable relationship between student teacher ratio and student achievement (Bosworth; Wenglinksy). The Bosworth study on t he effects of class sizes takes into account the characteristics of the students that make up the class (14). The class size is related to student achievement. When taking student demographic into account, the estimates suggest that the achievement of stud ents who are eligible for free or reduced lunch and female students is influenced more by smaller class sizes (15). Effects for both average achievement and the achievement gap are small, but the effects on the achievement gap are greater (19). Students wh o have lower
! %% achievement benefit more from smaller class sizes than students who have higher levels of achievement. Coates analyzes the education production function, including instructional time as a variable. The results suggest that instructional time for some subjects has an influence, but the influence is small (290). Coates finds that there is a small, positive relationship between instructional time for math and math test scores (287). The English and social studies instruction time is positively r elated to reading scores, but social studies instruction has a larger influence (286). Overall, instructional time has a small influence on achievement (290). The previous research for the education production function does not appear to illustrate consist ent relationships for education inputs and student achievement. As well, there are studies that illustrate that the relationships between education inputs and student achievement are not consistent across all of the academic subjects (Ram; Clotfelter, Ladd and Vigdor).
! %& Chapter 2: Education in the United States Financing the Public Education System There are three main levels of public education in the United States: elementary, secondary, and postsecondary (Snyder and Dillow 9). Between 1985 and 2011, p ublic school enrollment increased by 29% for elementary schools and 17% for secondary schools (1). Public schools are financed through revenue collected at the federal, state, and local level (Dixon vi). In the 2008 2009 academic year, there were 98,706 pu blic schools in the United States (Kober and Usher 21). The public education system in the United States is relatively decentralized, in comparison to other countries, as illustrated by the lack of a nation wide curriculum (23). "The central governments of many countries also have more authority than the U.S. federal government does in areas such as credentialing and hiring of teachers, requirements for graduation, and rules for compulsory education" (23). The federal government provides funds for the publi c education system, attached with some conditions such as improving the distribution of opportunity and improving academic achievement (26). In the 2007 2008 academic year, only 8% of the public funds for education were from the federal government; the rem ainder of the funds consisted of local (44%) and state (48%) funds (Kober and Usher 31). The majority of public education spending went towards instruction, which absorbed 61% of spending. The second largest was for maintenance and operations, utilizing 10 % of spending. This is followed by administration (8%), instructional staff services (5%), student support
! %' (5%), student transportation (4%), food service (4%), and other support services (3%) (36). In 2008 2009, the United States had 593.7 billion dollar s of education revenue for elementary and secondary public schools (Dixon xi). Seventy four billion dollars came from the federal government, 258.2 billion dollars came from the state governments, and 261.4 billion dollars came from the local governments. California had the largest revenue while the District of Columbia had the lowest revenue. In 2009 2010, total expenditure in the United States public education system was 602.6 billion dollars (xii). Out of the total expenditure, only 524 billion dollars w as current spending, 59.4 billion was capital outlay, and 19.3 billion was other. Of the 524 billion dollars of current spending, 317.8 billion went towards instruction (xiii). In 2010, the spending per pupil was $10, 615 while in 1992 spending per pupil w as $5,001 (xvi). In 2009, a stimulus package called the American Recover y and Reinvestment Act (ARRA) was passed (Rentner 1). In addition to stimulating other realms of the economy to protect the functioning of the economy, ARRA provided stimulus funds for primary, secondary and postsecondary schools. One function of this funding was to protect teacher positions. The funds provided in this package is an example of how the federal government can influence schools in a relatively decentralized system: "ARRA h as encouraged states to pursue a common reform agenda centered on the four assurances tied to the receipt of ARRA funds" (1). The reforms centered on improving the effectiveness of teachers, improving the performance of low
! %( performing schools, "adopting ri gorous standards and assessments" and "implementing statewide student data systems." It is important that there is an adequate amount of public school funding that will allow for the provision of a strong curriculum, trained teachers, and a strong adminis tration (Baker, Sciarra and Farrie 1). Different school populations have different needs that must be addressed and paid for, such as a student population made up primarily of students from a lower economic class. Each state has its own funding system, or "school funding formula'" (2). Thus some states have progressive funding, some states have regressive funding, and some do not show a clear pattern (17). Reforms In general, education reforms have been structured to increase equity, school choice, and us e of academic standards (Jennings 2). The reform movement with a focus on equity attempts to improve education for marginalized groups, such as economically disadvantaged children. Reform based on academic standards began in the 1980s and is strongly utili zed to present date (5 6). These reforms are also used to promote equity. A recent form of academic standard based reform is the 2002 No Child Left Behind (NCLB) Act NCLB is an attempt to improve the level of student achievement to the degree that 100% of students achieve at the proficient level by 2014 (Usher 1). In reviewing the progress it is found that 48% of schools did not meet adequate yearly progress (AYP) in 2011, which is higher than 2010 during which 39% of schools did not meet
! %) AYP (2). This is determined by a school's ability to meet annual measurable objectives (AMOs), which are set by individual states to measure performance. Five states and Washington, D.C. had 75% of their public schools not meet the 2011 AYP; these states were Florida, New Mexico, Massachusetts, South Carolina, and Missouri (3). In 2012, the U.S. Department of Education published the U.S. Department of Education FY 2012 Agency Financial Report This report illustrated the department's goals for the year of 2012. Two of the six goals were to "prepare all elementary and secondary students for college and career by improving the education system's ability to consistently deliver excellent classroom instruction with rigorous academic standards while providing effective support s ervices," and to "ensure and promote effective educational opportunities and safe and healthy learning environments for all students regardless of race, ethnicity, national origin, age, sex, sexual orientation, gender identity, disability, language, and so cioeconomic status" (17, 20). This department has an influence on the behaviors of education institutions, in part, through federal funding. For example, the "Teacher Incentive Fund" provides incentive for teachers and principals to work in high need schoo ls (17 8). Another example is the fact that the Department of Education "enforces civil rights laws that prohibit discriminationin our nation's schools, primarily in educational institutions that receive federal funds from the Department" (21).
! %* Testing a nd Eighth Grade Testing has played a larger role in the education system as a result of the focus on academic standards in education reform; "the major problem with standards based reform is that it has become test driven reform" (Jennings 5). Testing is u sed to see if schools are meeting the standards set by each individual state. For example, test results can be used to measure the achievement levels overall. Test results can be analyzed to measure the achievement levels of the heterogeneous student body by specific categories, such as race, economic class, gender, and age group. Using generalizations, each of the previously mentioned categories has various factors that should be considered in improving the education system Eighth grade, along with other middle school grades, has been a source of interest due to the "unique educational, social, and emotional needs" of adolescents (Chudowsky and Chudowsky "8 th Grade" 1). On a whole, states have illustrated progress for 8 th grade achievement. However, ther e is also an achievement gap between races, students from various economic classes, and genders at the 8 th grade level. Using states' test achievement (basic, proficient, and advanced) between around 2002 and 2009, Chudowsky and Chudowsky analyze the trend s for eighth grade achievement (3). For "basic and above," "proficient and above," and advanced, eighth grade had the largest percentage of states that illustrated gains in achievement for math and reading in comparison to fourth grade and high school (4). This is with the exception of the "basic and above" achievement gain for fourth grade math and the advanced achievement gain for fourth grade reading in which the two grades were tied with 89% and 83% of the states illustrating gains, respectively.
! %+ When analyzing 8 th grade performance by various categories based on race, economic class, and gender the achievement of 8 th grade students is proven to be inconsistent (Chudowsky and Chudowsky "8 th Grade") In 2009, there was a large achievement gap between di fferent groups of students at the advanced level of achievement. For example, 7% of black students reached the advanced level in math while 41% of Asian American and 24% of white students achieved at the advanced level (7). Further, only 9% of low income s tudents achieved at the advanced level in math. This data represents the states that had "sufficient data." In measuring the achievement gap at the advanced level for math and reading, between the years of 2002 and 2009 (some states have fewer years), ther e was a larger percentage of states that reported an increase in the achievement gaps between black and white students, Hispanic and white students, American Indian and white students, and low income and "not low income" students in comparison to a decreas e in the achievement gap or no change at all (8). There was a greater percentage of states that reported an increase in the achievement gap between male and female advanced reading achievement (8). For the male and female achievement gap, as measured by re ading performance, females performed better The percentage of states that had an increase in achievement gaps was highest for low income to not low income students in both reading and math. The percentage of states that had achievement gaps widen was grea ter in math than reading.
! %, De Facto Segregation In 2008 2009 academic school year, 90% of the nations 55 million students, inclusive of prekindergarden to 12 th grade were in public schools, with the South serving the largest percentage of students (Kober and Usher 3 4). By the 2020 2021 academic year, it is estimated that the public school enrollment will expand by 7% (5). Suburban schools serve the largest group of public education students (35%), followed by city schools (29%), rural schools (24%) and s chools in towns (12%) (6). In general, school districts with students from middle and upper income families have higher property wealth (Jennings 8). Local revenues expended on education are collected through property tax. In 2008, the racial composition of the student body population of public schools consisted of racial minorities, inclusive of Hispanic, black, Asian/Pacific Islander, and American Indian, that made up 45% of the population, while white students made up the other 55% of students (Kober a nd Usher 15). As measured by the number of students who receive free or reduced lunch, 45% of public school students are from a low economic class (18). "Students are eligible for free lunch if their family income does not exceed 130% of the federal povert y level and for reduced price lunch if their family income is above 130% but below 185%" (18). There is a low level of integration in the United States public education system, as measured by the proportion of students of different economic and racial back grounds in a school. Black, Hispanic, and American Indian students are concentrated in schools that serve a high number of impoverished students (Kober and Usher 8). The poverty
! &! level of the student is measured by whether or not students are eligible for the free or reduced price lunch program. Further, minority students attend schools with a high concentration of minority students, while white students attend schools with a high concentration of white students. Minority students in this study consist of b lack, Hispanic, Asian, Pacific Islander, American Indian, and Alaska Native people. For example, 74% of black students attend a school with 50% 100% of minority students and 8% of black students attend a school with 0 24% of minority students. On the other end, 14% of white students attend a school with 50 100% of minority students while 62% of white students attend a school with 0 24% of minority students. In 2001, males had a higher drop out rate than females. Racially, Hispanic people had a higher dropou t rate, 32% for males and 22% for females, followed by black people, 13% for males and 9% for females, and then white people, 8% for males and 7% for females (Freeman 56). Using the National Assessment of Educational Progress scores (the "long term trend a ssessment" and the "main NAEP"), Kober and Usher present the achievement level of public school students in the United States (39). These tests cover a range of subjects and are distributed to students from various ages and demographic backgrounds. For exa mple, using average scores for the long term trend assessment, there has been a significant increase in both reading and math scores for 9 year olds and 13 year olds between 1970 and 2008, but not for 17 year olds (39 40). Using average scores from the mai n NAEP, math scores between the years of 1990 and 2011 have increased for 4 th and 8 th grade while the reading scores for 4 th and 8 th grade between the years of 1992 and 2011 have "risen somewhat" (41 2). However,
! &$ when looking at the math and reading scores between the years of 2003 and 2011 for 4 th grade and 8 th grade, according to economic class, students who are not eligible for free or reduced price lunch have the highest scores in math and reading while those eligible for free lunch have the lowest (45) A Call to Action to Raise Achievement for African American Students calls into question the achievement gap specifically between black students and white students. The achievement gap illustrates the consequences of an inequitable distribution of educat ion opportuni ties and of de facto segregation in the education system (9). In 2008, the states in which black students had the lowest level of academic achievement in comparison to the other students are the states with schools that serve a student populat ion in which 90% of the students are black. In general, the average academic performance level of black students is low (4). Gender Inequalities The analysis of NAEP scores between 1992 and 2003 illustrate females in grades four, eight, and twelve achiev e higher than males in reading (Freeman 28). Scores from 1998 and 2002 illustrate that females also outperform males in writing. Reading achievement in 2008 was greater for girls than boys at the elementary, middle, and high school level (Chudowsky and Ch udowsky "Boys and Girls" 6). In addition, there were states in which the gap for male and female achievement was greater than 10 points. Overall, the number of males and females taking various math and science courses has increased between 1982 and 2000 (Freeman 60). In 2000, the percentage
! &% of females in some math and sciences courses, such as geometry and biology, was greater than the percentage of males in the courses. The inequalities of achievement in math for males and females between 1990 and 2003 w ere not large (30). Achievement levels across states from 2008 illustrate that there is not a consistent achievement gap in math (Chudowsky and Chudowsky "Boys and Girls" 1). Across states, girls and boys switched places as to which group achieved at a hi gher level for math, and the greatest difference between the male and female math achievement in a state was no more than 10%. South Carolina and Public Education In the 2010 2011 academic year, there were 725,838 students in South Carolina ("State Prof iles"). More than 53% of the students were white, 36.2% of the students were black, 6.4% of the students were Hispanic, 1.3% of the students were Asian, 0.1% of the students were Pacific Islander, and 0.3% of the students were American Indian/Alaskan Nati ve. A little over fifty four percent of the students were eligible for free or reduced price lunch. There were 1,228 schools and the expenditure per pupil was $9,143. The average student teacher ratio was 16.05 while the national average is 15.97. To meas ure the quality of the schools and districts, each school and district release an annual report card ( 2012 State Report Cards ) The report card illustrates the performance over the last five years for "absolute rating" and "growth rating" through the fol lowing qualifiers: at risk, below average, average, good, and excellent. These ratings are based on the schools and districts growth towards the "South
! && Carolina Performance Vision." This vision sets the goal for all students to graduate with the necessary skills and knowledge by 2020: "By 2020 all students will graduate with the knowledge and skills necessary to compete successfully in the global economy, participate in a democratic society and contribute positively as members of families and communities." The achievment of students in South Carolina public schools varies across the state, as illustrated by the district and school report cards There are multiple state assessments to measure the achievement level of public schools and students. These tests include the Palmetto Assessment of State Standards (PASS), the High School Assessment Program (HSAP), End of Course Examination Program (EOCEP), and the South Carolina Alternate Assessment (SC Alt) ("State Assessments" ). PASS is administered to third thro ugh eighth grade students to measure achievement in math, writing, English language arts, science, and social studies. However, not all of the previously mentioned subjects are tested at each grade level. The HSAP is administered in high school and student s must pass this test in order to graduate from high school. It assesses the student academic achievement in math and English language arts. The EOCEP is a state test for high school level core courses, such as U.S. History and the Constitution and English 1. SC Alt are for students with a disability that prevents student participation. The Nation's Report Card specific to South Carolina, illustrates the performance for the entire state of South Carolina using the results from the National Assessment of Ed ucational Progress ( "State Profiles"). The overall performance is illustrated for grades four and eight on the national math, science, writing, and
! &' reading assessment, as illustrated by the following achievement levels: below basic, basic, proficient, and advanced. For example, for eighth grade math in 2011, 30% of the students scored below basic, 38% scored basic, 25% scored proficient, and 7% scored advanced ("Mathematics 2011 State Snapshot"). Overall, the average score for South Carolina, 281, was not s ignificantly different from the national average score, 283. This report card also illustrates the varied achievement amongst various groups. These various group s are students who identify as White, B lack, Hispanic, Asian, American Indian/Alaskan Native, a nd students who identify with two or more races. Various groups also include students who are male, female, and students who are eligible for free or reduced lunch. While the female and male average scores did not differ significantly, there were other ac hievement gaps illustrated by the 8 th grade math achievement scores in 2011. Similar to the 33 point gap between black and white students in 1992, white students scored 30 points more on average than black students. White students also scored 20 points mor e than Hispanic students. In both 1996 and 2011, students who were not eligible for free or reduced price lunch had an average score that was 26 points higher than students who were eligible for free or reduced price lunch. The achievement gaps for eighth grade reading illustrated a similar relationship between black and white students (24 point gap), Hispanic and white students (13 point gap), and students who are eligible for free/reduced price lunch and students who are not eligible (21 point gap) ("Rea ding 2011 State Snapshot"). However, as opposed to the female male math gap, there was a gap for average scores
! &( between females and males. Males scored 10 points lower, on average, than females. Over all South Carolina had an average score of 260 and the U nited States had an average score of 264. Eighth grade science scores illustrated an achievement gap between black and white students (35 points) Hispanic and white students (24 points), and students are eligible for free/reduced price lunch and students who are not (26 points) ("Science 2011 Snapshot"). The average male and female scores were not significantly different (3 points). Overall, South Carolina had an average of 149, which is not significantly different from the average score of the United Stat es, which was 151. The most recent report for writing NAEP results in South Carolina is from 2007 ("Writing 2007 State Snapshot"). Overall, South Carolina had an average score of 148 while the United States had an overall average score of 154. The black wh ite achievement gap was present with an average 18 points difference. The Hispanic white achievement gap was present with an average 16 points difference. Students who were not eligible for free or reduced price lunch achieved an average score 19 points hi gher than students who were eligible for free or reduced price lunch. Financing The total revenue in 2009 for education is less than the total amount expended. The revenue for public education in South Carolina consists of revenue collected at the state local, and federal level ("SC Education" 1). In FY 2009, the state revenue was the largest portion of the public education revenue, with $3,218,060,614, or 47% of the total $7,552,379,873. Local revenue made up 43% of
! &) the revenue for public education and federal revenue makes up 10% of the revenue for public education. Federal, state, and local revenue come from multiple sources. In FY 2011, the General Fund made up 75% of the state appropriation. In general, a significant portion of local revenue is deri ved from the local property taxes (6). Congress determines federal revenue (1). In reviewing the overall state budget in South Carolina for 2010 2011, the state had a total of $21.1 billion budgeted ( FY10 11 Finance ). The South Carolina budget consists of General Funds, Federal Funds, and Other Funds. The General Funds portion of this budget, which mostly consists of income and retail sales tax revenue, contributes $5.1 billion to the total South Carolina state budget. Of the General Funds, 47.2% is use d for K 12 and higher education, with 36% funding K 12 education and 11.2 % funding higher education. So, the General Fund contributed $1,831,503,698 to K 12 education in 2010 11. Revenue from the South Carolina's Education Lottery Account also funds K 12 education, in addition to higher education. State revenue for public education is "distributed either by a categorical appropriation or through a per pupil weighting" ( "SC Education" 1). While per pupil weighting is dependent on the demographic of the stu dent population, categorical funding is used to fund a service or program. For example, in South Carolina, the Education Finance Act of 1977 (EFA) is set to ensure that every public school student has access to "at least minimum educational programs and s ervices appropriate to the student's needs, and which are substantially equal to those available to other students with similar needsregardless of geographic differences and local economic factors"
! &* (2). Thus, this act is to ensure that all students are al lotted funding to, at minimum, address their needs. The state provides 70% of the funds for EFA, and the other 30% is funded by local revenue. The amount that the districts contribute is depende nt upon "its relative tax paying ability." In the EFA, weigh ted pupil units (WPU) are used in order to determine how much funding is needed based on costs related to student classifications (3). The weighting of the student is relative to that of the base student, which is 1.00. The base student costs are costs ass ociated with students that require minimum funding. For example, grades 4 8, or elementary school students, have the base student weighting 1.00. Kindergarten's weighting is 1.30, primary school students' (grade 1 3) weighting is 1.24, and high school stud ents' weighting is 1.25. Weightings are also used to distribute an appropriate amount of funding to students with various handicaps, homebound students, and vocational students. This system is designed to meet the costs of addressing various needs of the s tudent body. The money allotted to the EFA is not the only state public education funding. For example, in FY 2011, money from the General Fund made up 75% of the state appropriation for public education, and 54.8% of the money from the General Fund money devoted to education was devoted to the Education Finance Act ("SC Education" 1 2). Besides the Education Finance Act the General Fund contributed to variables including, but not limited to, the school bus transportation system and instructional material s. Over $1.1 billion was allotted for the EFA in 2011 2012 (Jinette 5). "The purpose of this act, according to its legislative background, can be summarized in
! &+ three words: adequacy, equality, and accountability" (6). The State contributes, to each distri ct, the amount of funding necessary to cover the difference between the funding necessary for the foundation program and the amount of funding that must be locally provided. The local contribution is dependent, in part, on the district's taxpaying capacity To determine the amount of funding provided for a district, the weighting factor is taken into consideration by multiplying "the average daily membership for each student classificationby the weighting factor for the respective classification." This res ult, known as the weighted pupil units, is multiplied by the base student costs to determine the costs for the foundation program. Thus, "eighty five (85) percent of the fundsmust be spent in direct and indirect aid of the specific program (classification ) that serves the students who generated the funds." The Education Improvement Act of 1984 (EIA) is an attempt to improve public education in South Carolina, and it included a one cent increase in state sales tax to increase funding ( "SC Education" 5 ; Ji nette 9). In addition, local school districts must increase the local tax revenue effort by at least the level of inflation. This plan included improving the physical education facilities, improving teaching and testing basic skills, and improving student performance through the elevation of academic standards. Other factors of this act included improving the teaching profession, fiscal efficiency, productivity recognition, and partnerships with the school, community, businesses, and parents. Programs funde d by this act includes, but is not limited to, programs for students at risk of failing, high achieving students, adult education, early childhood education, assessment and testing, and teacher supplies.
! &, Various sources contribute to local revenue, includ ing property tax ( "SC Education" 6). The function of the districts in determining the level of local revenue, dependant on the control allotted to the school district to set millage rates, varies across the state. Twenty three districts are fiscally autono mous, while the other sixty two are met with restrictions concerning the development of a millage rate. The South Carolina Education Accountability Act of 1998 marked the formation of the performance based accountability system in South Carolina (Jinette 11). According to this act, the responsibility of the improvement of student and school performance belongs to the "Governor, the General Assembly, the Education Oversight Committee, the State Board of Education, the South Carolina Department of Education local school boards, colleges and universities, administrators, teachers, and parents" (11). The accountability system was developed to improve the academic performance. Performance is illustrated through annual school and district report cards. This a ct is also set up to address the weaknesses of the public education system, after locating them. For example, this act requires districts to "target assistance to low performing schools" (11). Overall, the accountability system is supposed to "stimulate qu ality teaching and learning practices." Thus, resources should be provided to improve the overall quality of public education. Districts receive funds for "students at risk of school failure" based on the districts poverty and on the number of students w ho do not meet state standards for reading or math (Jinette 46). Eighty five percent or more of this funding must be used on instruction and instructional support for the students at risk. This includes
! '! programs directed at the family, such as family liter acy programs. Actions include, but are not limited to, reducing class sizes, literacy and parenting programs for families, a nd summer school programs (47).
! '$ Chapter 3: Methodology Data The data used in this study was retrieved from the South Carolina Department of Education (SCDE) website. The data set was compiled by data extracted from multiple SCDE sources. These sources include the 2012 report cards for the individual schools and the 2012 PASS excel file ( 2012 State Report Cards "; "2012 Palmetto Assessment of Sta te Standards (PASS) Test Scores" 2011 12 data file). The student achievement on the PASS (Palmetto Assessment of State St andards) test was chosen because it is one of the state assessment tests used to measure student achievement and used for accountabil ity reasons. Since 2009, t he test has assessed p ublic school stude nts in grades 3 8 Students with disabilities that cannot be accommodated are required to take the South Carolina Alternate Assessment. The report cards rank schools based on their level of progress. Schools are ranked as excellent, good, average, below average, and at risk. As stated in the report cards, the st andards being used are set by the "2020 SC Performance Vision." The following are the goals of the vision: "by 2020 all students will graduate with the knowledge and skills necessary to compete successfully in the global economy, participate in a democrati c society and contribute positively as members of families and communities." The data collected from the individual school report cards were manually entered into the excel spreadsheet. The cross sectional data will be used in a linear regression to anal yze the relationship between education inputs and student achievement. Regressions were developed for the five different academic subjects being considered in this study. The
! '% 8 th grade PASS tests cover English Language Arts, Mathematics, Science, Social St udies, and Writing ("Palmetto Assessment of State Standards (PASS) Grades 3 8"). English language arts, mathematics, and writing tests are taken by all test takers while science and social studies are randomly assigned to students. The random assignment fo r science and social studies tests lead to an approximate equal distribution. The scores for the PASS exam are categorized as "Not Met," "Met," or "Exemplary." Scores are categorized as "Not Met" when the scores do not meet the grade appropriate standard. Scores are categorized as "Met" when scores do meet the grade appropriate standard. Scores are categorized as "Exemplary" when scores exceed the grade appropriate standard. Table 1.1 PASS Score Categories PASS Subject Not Met Met Exemplary English Langu age Arts 300 599 600 648 649 900 Mathematics 300 599 500 656 657 684 Science 300 599 600 650 651 900 Social Studies 300 599 600 655 656 900 Writing 300 599 600 650 651 900 Source: South Carolina State Government. Department of Education. PASS Cut off Scores 2011.
! '& analyzing the data, the sample size is not consistent. Thus the sample size for each model is contingent on whether any of the schools are missing any of the variables necessary for the model. Table 1.2 Main Analysis Dependent Variables Mean, Minimum, and Maximum Variable N Mean Minimum Maximum Elapct Mathpct Scipct Socpct Writpct 288 284 274 278 291 67.176 66.199 73.266 68.923 71.795 23.100 18.600 24.000 20.00 0 25.000 100.000 100.000 100.000 100.000 100.100 Table 1.3 Schools in which more than 50% of Test Takers are Eligible for FRL Dependent Variables Mean, Minimum, and Maximum Variable N Mean Minimum Maximum Elapct Mathpct Scipct Socpct Writpct 143 137 134 137 137 58.880 57.473 65.397 68.923 63.699 23.100 18.600 24.000 20.000 25.000 86.400 92.900 93.300 92.300 92.900 Tables 1.2 and 1.3 illustrate the mean, minimum, and maximum for student achievement, as measured by the percent of test takers that met or exceeded the standards for the PASS exam by school. As seen in the tables, the schools in which more than 50% of the test takers are eligible for FRL, the maximum student
! '' achievement is less than the student achievement for the sample of the main a nalysis. As well, the mean percent of student achievement is lower for all subjects except Social Studies. For the sample of the main analysis, the mean average expenditure per student is $7,824, with a range from $3,745 to $45,759. 1 The mean of the perce nt of teachers returning is 84 % with a range from 49% to 96%. For English Language Arts, the percent of Black test takers ranged from 0 to 100%, with a mean of 41.896. The percent of Asian test takers ranged from 0 to 6.340%, with a mean of 0.903%. The pe rcent of test takers who identify with another minority racial identity range from 0 to 39.444%, with a mean of 7.062%. The percent of test takers who identify as female range from 0 to 100%, with a mean of 48.547%. The percent of test takers who are eligi ble for FRL range form 0 to 100%, with a mean of 60.298%. For English Language Arts in schools in which more than 50% of the test takers are eligible for FRL, the percent of Black test takers range from 8.182 to 100%, with a mean of 60.190%. The percent o f Asian test takers range from 0 to 5.555%, with a mean of 0.508%. The percent of test takers who identify with another minority racial identity range from 0 to 39.444% with a mean of 6.952%. The percent of test takers who identify as female range from 0 t o 75 % with a mean of 48.023. The percent of test takers eligible for FRL range from 60.352 to 100%, with a mean of 77.803. The mean, minimum, and maximum of school inputs varied across subject tests. For English Language Arts, the mean average expenditure per student $8,555, !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! 1 See appendix for the independent variable descriptive statistics tables.
! '( ranging from $3,745 to $21,939. The mean percent of teachers returning was 81.75% and the range was from 48.9% to 95%. The mean average expenditure per student is greater in schools in which more than 50% of the test takers are eligib le for FRL. Also, the percent of black test takers is greater in the schools in which more than 50% of the test takers are eligible for FRL. Education Production Function Model The model applied to each subject test is as follows: !"# ! !"#! !"#$%&'%( !"#$ !"#$ !"#"$% !"#$ !"# !"#$%&'()"%*"+#"", !"#$%&"'%() !"#$%&' !"#$ !"#$$!%& !"#$ !"#$!%&"'(') !" !"#$% !"# !! !"#!$ !"# !" !" !" !"# !" !"#$%" !"# !" !"# !"# = school pct = percent of 8 th grade test takers who met or exceeded state standards on the subject test PASS test (ela; math; sci; soc; writ) Y2012= Expenditure per student (in thousands) ExpendIns= Percent of expenditures used for instruction Prime_time = prime instructional time Salary = Teacher salary (in thousands) Prof_dev = Professional Development days per teacher PerAdvancedDegrees = Percent of Teachers per school with advanced degrees StudentTeacherRatio = Student Teacher Ratio TeacherAttend = Te acher attendance rate TeachersReturning = Percent of teachers returning from previous year N_black_pct = Percent of 8 th grade black students who took the subject PASS test (ela; math; sci; soc; writ) N_asian_pct = Percent of 8 th grade Asian students who to ok the subject PASS test (ela; math; sci; soc; writ) N_other_pct = Percent of 8 th grade racial or ethnic minority students (excluding black and Asian) who took the subject PASS test (ela; math; sci; soc; writ) N_female_pct = Percent of 8 th grade female stu dents who took the subject PASS test (ela; math; sci; soc; writ) N_sub_pct = Percent of 8 th grade students eligible for free or subsidized lunch who took the subject PASS test (ela; math; sci; soc; writ)
! ') The expected coefficients will be consistent acros s all five academic su bjects and for both regression analyses This study is designed to test the following hypotheses: 1) Expenditure per student is positively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS te st; 2) Percent of expenditures used for instruction will be positively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test; 3) Prime instructional time will be positively related to the percent of 8 th grade test t akers who met or exceeded state standards on the PASS test; 4) Teacher salary will be positively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test; 5) The number of professional development days per teacher will be positively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test; 6) Percent of teachers with advanced degrees will be positively related to the percent of 8 th grade test takers who met or exceeded state stan dards on the PASS test; 7) The student teacher ratio will be negatively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test; 8) Teachers' attendance rate will be positively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test; 9) Percent of teachers returning from the previous year will be positively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test; 10) Percent of test take rs that are black will be negatively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test; 11) Percent of test takers that are Asian will be positively related to the percent of 8 th grade test takers who met or e xceeded state standards on the PASS test; 12) Percent of test takers that are identify with another racial or ethnic minority group (excluding black or Asian) will be negatively related to the percent of 8 th grade test takers who met or exceeded state standard s on the PASS test; 13) Percent of test takers that are female will be positively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test; 14) Percent of test takers that are eligible for free or reduced price lunch are negatively related to the percent of 8 th grade test takers who met or exceeded state standards on the PASS test. In order to analyze the relationship between all independent and dependent variables in schools with a larger population of test takers that are eligible for FRL, each regression will be run again. The samples used in these regressions will include
! '* schools in which more than half of the 8 th grade students that took the PASS exam were eligible for free or reduced price lunch. This study will us e probability values, also known as p values, at .10, .05, and .01 significance level s to determine whether or not the results are statistically significant. Data Transformations The data was transformed in multiple ways. In order to create a data set tha t was in the appropriate format, a number of the variables had to be reformatted. The demographic variables were originally stacked; in order to use these variables, they were extracted from the original PASS excel spreadsheet, transposed into columns and merged with the working dataset. In addition to the data that was in the original PASS spreadsheet, data was collected from individual report cards and manually entered into an excel spreadsheet. The data collected from individual report cards was also me rged with the working dataset. After organizing the data for each school, the racial category "other" was created. This is inclusive of American Indian students, Pacific Islander students, Hispanic students, and students who identify with more than one rac e or ethnicity. Second, the demographic data, inclusive of data for student race, gender, and economic class, data was transformed from whole numbers to percentages. Third, the demographic data that was left blank was assigned a zero or zero percent. Other minor adjustments to independent variables included dividing salary and expenditure per student by one thousand so that the measures would be in thousands. The
! '+ percentage measures for demographics were changed from being decimals to percentages. For the dependent variables, the measure for each subject is the percentage of 8 th grade PASS test takers who met or exceeded state standards. The results were originally divided into three different categories: percent of test takers who did not meet standards, p ercent of test takers who met standards, and percent of test takers who had exemplary scores. For the models used in this study, the percent of test takers who met the standards and the percent of test takers that were exemplary were added together. Thus, the dependent variable measures the percentage of test takers that met or exceeded the standards. Data Limitations One of the weaknesses of this data set was the missing data. Missing data posed a number of complications in trying to manipulate the data. It also complicated the attempt to utilize a consistent number of schools in the sample for the regressions. Missing data reduces the possible sample size. The next set of weaknesses is a result of the nature of the data. The data being used was aggregate d at the school and grade level as opposed to having individual student data. Aggregation mutes details that can produce better estimates. Another limitation to the data is the fact that the student achievement was not only based on the achievement of test takers who were continuously in the school from the 45 th day of school, but could also include the achievement level of students who later enrolled (Hearn).
! ', Diagnostics The data in this set was tested for heteroskedasticity and multicollinearity. Heteros k edasticity ( !"# ! ) exists when errors are not dispersed equally enough that the variance of the error term is not constant (Baddeley and Barrowclough, 141). For example, this can occur when a data set has outliers. The residuals and predic ted values for each model were plotted in order to visually analyze the level of heteroskedasticity. The results from the White test illustrate whether or not the variance of residuals is homogenous ("Regression with SAS Chapter 2 Regression Diagnostics") If the p value is greater than 0.05, then the variance of residuals is homogenous. As illustrated by the White tests and the tables, the variance of residuals is homogenous for all models except science and writing. 2 Multicollinearity exists when there is a high correlation between independent variables. Imperfect multicollinearity is illustrated by a high correlation coefficient that is not equal to (Baddeley and Barrowclough, 119). This affects the ability to derive the estimate s of the indepen dent variables that are highly correlated as well as the reliability of the estimations, increasing the chances that you do not reject a false null hypothesis (127). To analyze the multicollinearity of the variables for each model, the variance inflation factor (vif) was measured ("Regression with SAS Chapter 2 Regression Diagnostics"). If the vif is less than 10, then multicollinearity is not a large issue for the variable being considered. Multicollinearity is not a large issue for any of the variables. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! 2 The results for the diagnostic tests can be found in the appendix.
! (! Chapter 4: Results This section will present the parameter estimates for each variable which were measured at the school level. Fourteen different independent variables were analyzed in five subject areas. For the main analysis, the maximum number o f significant variables is 6 for Mathematics and the minimum is 2 for Science. For the analysis in which more than 50% of the test takers were eligible for FRL, the maximum number of significant variables is 4 for Mathematics. The minimum number of signifi cant variables is 2 for English, Science, and Writing. In general, the hypothesis was that school inputs would have a favorable relationship with student achievement. The hypotheses for the control variables varied: the percent of female students and Asia n students are expected to relate positively to student Table 2.1 Model 1 Results : English Language Arts a Variable Parameter Estimate Standard Error p value Intercept 19.30588 31.58520 0.5417 Y2012_t 0.21484 0.33862 0.5264 ExpendIns 0.11936 0.10720 0 .2667 Prime_Time 0.00907 0.11266 0.9359 Salary_t 0.30124 0.16995 0.0777 Prof_Dev 0.03424 0.08230 0.6778 PerAdvancedDegrees 0.04466 0.05044 0.3769 StudentTeacherRatio 0.09255 0.11397 0.4176 TeacherAttend 0.44957 0.31125 0.1500 TeachersReturning 0.19 456 0.07973 0.0154 ElaN_black_p 0.06603 0.03385 0.0523 ElaN_asian_p 0.24896 0.45439 0.5843 ElaN_other_p 0.00259 0.09169 0.9775 ElaN_female_p 0.17205 0.08520 0.0446 ElaN_sub_p 0.37095 0.04399 <.0001 a. Note: 241 Observations were used in this regres sion analysis. The adjusted R square equals 0.6632.
! ($ achievement while the other controls have a negative relationship to student achievement. In the main analysis, the hypotheses are correct for average teacher salary in English Language Arts and Math, as well as teacher's returning rate for all subjects, excluding Science. The hypotheses are also correct for the percent of Black students and the percent of students eligible for FRL in all subjects. The hypothesis is also correct for the percent of female students in English Language Arts, Social Studies, and Writing. For the secondary analysis, the hypothesis is correct for prime instructional time for all subjects excluding Social Studies. The hypothesis is correct for teacher's returning rate f or Math, Social Studies, and Writing. The hypothesis is also correct for the percent of Black students for Math and Science, percent of female Table 2.2 Model 2 Results : Mathematics a Variable Parameter Estimate Standard Error p value Intercept 1.78640 42 .23288 0.9663 Y2012_t 0.90394 0.45856 0.0499 ExpendIns 0.36871 0.13998 0.0090 Prime_Time 0.12854 0.14754 0.3846 Salary_t 0.61508 0.22400 0.0065 Prof_Dev 0.14382 0.10904 0.1885 PerAdvancedDegrees 0.02299 0.06616 0.7285 StudentTeacherRatio 0.02605 0.15014 0.8624 TeacherAttend 0.50884 0.41853 0.2254 TeachersReturning 0.30335 0.10595 0.0046 MathN_black_p 0.12294 0.04493 0.0067 MathN_asian_p 0.67834 0.56542 0.2315 MathN_other_p 0.10641 0.12140 0.3817 MathN_female_p 0.11757 0.11325 0.3003 MathN _sub_p 0.28900 0.05754 <.0001 a. Note: 238 observations were used in this regression analysis. The adjusted R square equals 0.5817.
! (% students for English and Social Studies, and the percent of students eligible for FRL for Social Studies. English Langua ge Arts The school inputs for the English Language A rts model that a re statistically significant are teacher salary at the .10 level of significance and the percent of te achers returning at the .05 level of significance. The control variables that are als o significant are the percent of students t aking the test who identify as B lack at the .05 level of significance the p ercent of students taking the test who identify as female at the .05 level of significance, and the percent of students who are qualified for FRL at the .01 level of significance. For every $1000 increase in salary there is a 0.30 Table 2.3 Model 3 Results : Science a Variable Parameter Estimate Standard Error p value Intercept 43.22073 38.66183 0.2648 Y2012_t 0.50045 0.46284 0.2808 Exp endIns 0.07898 0.13274 0.5525 Prime_Time 0.01581 0.13396 0.9062 Salary_t 0.13057 0.24179 0.5897 Prof_Dev 0.14896 0.09799 0.1299 PerAdvancedDegrees 0.08906 0.07002 0.2048 StudentTeacherRatio 0.10710 0.14711 0.4674 TeacherAttend 0.36591 0.37383 0.328 8 TeachersReturning 0.13158 0.09982 0.1889 SciN_black_p 0.17918 0.03866 <.0001 SciN_asian_p 0.05368 0.46773 0.9087 SciN_other_p 0.01851 0.10293 0.8574 SciN_female_p 0.10900 0.08763 0.2149 SciN_sub_p 0.31497 0.05011 <.0001 a. Note: 232 observatio ns were used for this regression analysis. The adjusted R square equals 0.5752.
! (& percentage point increase in the student achievement as measured by the percent of students who meet or exceed state standards for the PASS exam. For every 1% increase in teac h ers returning, there is a 0.20 percentage point increase in s tudent achievement. For every 1% increase in test takers who ide ntify as Black, there is a 0.07 percentage point decrease in student achievement. A 1% increase in test takers who ide ntify as fem ale leads to a 0.17 percentage point increase in student achievement. A 1% increase in test takers who are eligible for FRL red uces student achievement by 0.37 percentage points Thus, the estimate for percent of test takers who are eligible for FRL reduce student achievement has the greatest magnitude in examining the English language arts PASS exam data. The greatest magnitude for a positive parameter estimate is for the percent of teachers returning. Table 2.4 Model 4 Results : Social Studies a Variable P arameter Estimate Standard Error p value Intercept 20.63917 46.24580 0.6558 Y2012_t 0.70119 0.55305 0.2062 ExpendIns 0.09863 0.16008 0.5385 Prime_Time 0.05755 0.16223 0.7231 Salary_t 0.31235 0.29601 0.2925 Prof_Dev 0.00421 0.11905 0.9718 PerAdvanc edDegrees 0.05108 0.08542 0.5504 StudentTeacherRatio 0.19050 0.17377 0.2742 TeacherAttend 0.37634 0.45408 0.4081 TeachersReturning 0.45998 0.11611 0.0001 SocN_black_p 0.10430 0.04759 0.0294 SocN_asian_p 0.23041 0.52465 0.6610 SocN_other_p 0.12629 0 .11915 0.2904 SocN_female_p 0.15813 0.09506 0.0977 SocN_sub_p 0.36369 0.06009 <.0001 a. Note: 234 observations were used in this regression. The adjusted R square equals 0.5093.
! (' Mathematics The expenditure per student was significant at a .05 level o f significance. The percent of the expenditure on instruction, th e teacher's salary, and the p ercentage of teachers returning are significant at the .01 level of significance. T he percent of tes t takers who identify as Black and the percent of takers tha t are eligible for FRL are stati stically significant at the 0.01 level of significance. For every $1000 increase in expenditu re per student, there is a 0.90 percentage point decrease in the student achievement. For every 1% increase in the expenditure on i nstruction, there is a 0.37 percentage point decrease in the student achievement. For every $1000 increase in teacher salary, there is a 0.62 percentage point increase in the student achievement. For every 1% increase in teachers returning, there is a 0.30 percentage point i ncrease Table 2.5 Model 5 Results : Writing a Variable Parameter Estimate Standard Error p value Intercept 34.63477 33.26787 0.2989 Y2012_t 0.10612 0.358 87 0.7677 ExpendIns 0.04511 0.11397 0.6926 Prime_Time 0.00597 0.11963 0.9603 Salary_t 0.10992 0.18017 0.5424 Prof_Dev 0.05119 0.08739 0.5586 PerAdvancedDegrees 0.00181 0.05344 0.9730 StudentTeacherRatio 0.18863 0.12108 0.1206 TeacherAttend 0.29286 0.32912 0.3745 TeachersReturning 0.25844 0.08464 0.0025 WritN_black_p 0.06816 0.03577 0.0580 WritN_asian_p 0.61717 0.47155 0.1919 WritN_other_p 0.13415 0.09588 0.1631 WritN_female_p 0.16701 0.08961 0.0637 WritN_sub_p 0.32238 0.04643 <.0001 a. N ote: 242 observations were used in this regression analysis. The adjusted R square equals 0.6119.
! (( in student achievement. For every 1% increase in the test takers who ide ntify as Black, there is a 0.12 percentage point decrease in student achievement. For every 1% increase in the percent of test takers el igible for FRL, there is a 0.29 p ercentage point decrease in student achievement. In M ath, the parameter estimate for expenditure per student had the greatest magnitude. Other Estimates There were not any statistically significant school inputs for the student achievement in Science, S ocial Studies, or Writing that were not mentioned in either Table 2.6 Model 1 Results : English Language Arts where more than 50% are eligible for FRL a Variable Parameter Estimate Standard Error p value Intercept 3.77312 59.24645 0.9494 Y2012_t 0.47111 0.49261 0.3420 ExpendIns 0.14866 0.19479 0.4477 Prime_Time 1.56697 0.61688 0.0131 Salary_t 0.47894 0.37458 0.2050 Prof_Dev 0.02109 0.15061 0.7737 PerAdvancedDegrees 0.12862 0.11993 0.2870 StudentTeacherRatio 0.10918 0.21660 0.6157 TeacherAttend 1 .11963 0.78154 0.1561 TeachersReturning 0.16110 0.13842 0.2482 ElaN_black_p 0.12130 0.08258 0.1461 ElaN_asian_p 1.94556 1.20196 0.1097 ElaN_other_p 0.03936 0.19494 0.8405 ElaN_female_p 0.26788 0.15513 0.0883 ElaN_sub_p 0.20272 0.16196 0.2146 a. Note: 90 observations were used in this regression analysis. The adjusted R square equals 0.3067.
! () the English Language Arts or Math results. However, expenditure per student, percent of expenditure on instruction, and teacher salary were not statistical ly significant for Science, Social Studies, or Writing. The estimate for the percent of female students was not significant for Science. The estimate for the variable measuring the percent of teachers returning is consistently positive and statistically si gnificant, except for t he S cience analysis. The only estimates that were significant across all five subject tests are demographic control variables: percent of Black students and percent of students eligible for FRL. Table 2.7 Model 2 Results : Mathematics where more than 50% are eligible for FRL a Variable Parameter Estimate Standard Error p value Intercept 30.09777 81.09603 0.7116 Y2012_t 0.92603 0.67142 0.1722 ExpendIns 0.49857 0.25295 0.0526 Prime_Time 1.75437 0.82493 0.0369 Salary_t 0.50909 0. 49441 0.3067 Prof_Dev 0.22557 0.20066 0.2648 PerAdvancedDegrees 0.18462 0.15889 0.2491 StudentTeacherRatio 0.14922 0.28776 0.6057 TeacherAttend 0.91872 1.09443 0.4040 TeachersReturning 0.38942 0.18515 0.0390 MathN_black_p 0.18101 0.10868 0.1002 Ma thN_asian_p 1.08447 1.53461 0.4821 MathN_other_p 0.07249 0.26008 0.7813 MathN_female_p 0.23614 0.20779 0.2596 MathN_sub_p 0.19599 0.20974 0.3532 a. Note: 86 Observations were used in this regression analysis. The adjusted R square equals 0.3284
! (* More than 50% Results Th e results differed in the regressions that were run using data for schools in which more that 50% of the test takers were eligible for FRL. For English L anguage Arts, prime time is significant at the .01 level of significance. T he percent of test takers that identified as female is statistically significant at the .10 level of significance. For a 1% increase in p rime time, there is a 1.57 percentage point increase in student achievement. For a 1% in test takers who iden tify as fem ale, there is a 0.27 percentage point i ncrease in student achievement. In M ath, the perce nt of expenditure that was spent on instruction, the percent of teacher's returning, prime instructional time and the percent of test takers that Table 2.8 Model 3 R esults : Science where more than 50% are eligible for FRL a Variable Parameter Estimate Standard Error p value Intercept 40.08020 76.02294 0.5998 Y2012_t 0.91698 0.71787 0.2058 ExpendIns 0.07675 0.23887 0.7490 Prime_Time 2.03636 0.78903 0.0120 Salary_t 0.29584 0.53501 0.5821 Prof_Dev 0.25364 0.17975 0.1628 PerAdvancedDegrees 0.00725 0.15829 0.9636 StudentTeacherRatio 0.21414 0.29320 0.4677 TeacherAttend 1.64561 1.01454 0.1094 TeachersReturning 0.08807 0.17714 0.6207 SciN_black_p 0.29511 0.10490 0.0064 SciN_asian_p 1.40959 1.30989 0.2857 SciN_other_p 0.11848 0.23031 0.6086 SciN_female_p 0.16524 0.16807 0.3290 SciN_sub_p 0.26590 0.18235 0.1494 a. Note: 83 observations were used in this regression analysis. The adjusted R square equ als 0.3473.
! (+ identified as black are statisticall y significant. A 1% increase in expenditure spent on instruction will result in a 0.50 percentage point decrease in student achievement. A 1% increase in prime instructional time will lead to a 1.75 percentag e point increase in student achievement. A 1% increase in teachers returning will result in a 0.39 percentage point increase in student achievement. A 1% increase in the test takers who id entify as Black leads to a 0.18 percentage point decrease in student achievement. For Science, Social Studies, and Writing there are not any statistically significant variables that were not already highlighted in English Language Arts, M ath, or both. The percent of teachers returning is consistently statistically signif icant Table 2.9 Model 4 Results : Social Studies where more than 50% are eligible for FRL a Variable Parameter Estimate Standard Error p value Intercept 84.61561 80.63566 0.2978 Y2012_t 0.59430 0.75568 0.4344 ExpendIns 0.36311 0.26482 0.1749 Prime_Tim e 1.36295 0.85112 0.1140 Salary_t 0.23073 0.56294 0.6832 Prof_Dev 0.06695 0.19159 0.7279 PerAdvancedDegrees 0.03109 0.16941 0.8549 StudentTeacherRatio 0.11158 0.29603 0.7074 TeacherAttend 0.16844 1.06227 0.8745 TeachersReturning 0.55591 0.18043 0.0030 SocN_black_p 0.11828 0.09547 0.2197 SocN_asian_p 0.85749 1.32525 0.5198 SocN_other_p 0.00316 0.24218 0.9896 SocN_female_p 0.37920 0.16272 0.0228 SocN_sub_p 0.29965 0.17702 0.0951 a. Note: 82 observations were used in this regression anal ysis. The adjusted R square equals 0.2832.
! (, for all subjects, except English Language Arts and Science. Overall Significance Tables 2.11 and 2.12 summarize the significant variables for the main and secondary analyses. For the main analysis, the school in put with the greatest number of statistically significant estimates is teacher returning rate. The percent of test takers that are black and the percent of test takers eligible for FRL have the most significant estimates overall. For the secondary analysis the school input that has the greatest number of statistically significant parameter estimates is prime instructional time. Prime instructional time only has statistically significant variables in the secondary analysis. Table 2.10 Model 5 Results : Writi ng where more than 50% are eligible for FRL a Variable Parameter Estimate Standard Error p value Intercept 30.56840 64.19480 0.6353 Y2012_t 0.16605 0.55655 0.7663 ExpendIns 0.11523 0.21711 0.5972 Prime_Time 1.40396 0.69375 0.0466 Salary_t 0.12857 0.4 1978 0.7602 Prof_Dev 0.06596 0.16765 0.6951 PerAdvancedDegrees 0.18972 0.13278 0.1572 StudentTeacherRatio 0.35995 0.24616 0.1479 TeacherAttend 1.40379 0.88115 0.1153 TeachersReturning 0.34630 0.15523 0.0287 WritN_black_p 0.01131 0.09201 0.9025 Writ N_asian_p 1.47395 1.40297 0.2968 WritN_other_p 0.00085159 0.21698 0.9969 WritN_female_p 0.26528 0.17544 0.1347 WritN_sub_p 0.26800 0.17979 0.1402 a. Note: 90 observations were used in this regression analysis. The adjusted R square equals 0.2665.
! )! Table 2.11 Significant Parameter Estimates For Mai n Analysis ab Independent Variable Dependent Variable: % of students who met or exceeded state standards ------------------------------------------------------------------------------------------------------------------------------------------English Math Science Social Studies Writing N=241 N=238 N=232 N=234 N=242 Expenditu re Per Student -0.903** ---Expenditure on Instruction -0.369*** --Teacher Salary 0.301* 0.615*** ---Teacher's Returning Rate 0.195** 0.303*** -0.460*** 0.258*** Percent of Black Students 0.066** 0.123*** 0.179*** 0.104** 0.068* Percent of Female Students 0.172** --0.158* 0.167* Percent of Students Eligible for FRL 0.371*** 0.289*** 0.315*** 0.364*** 0.322*** -------------------------------------------------------------------------------------------------------------------------------------------a. Note: Significance Levels: .10, ** .05, *** .01 ./ The variables that are insignificant for all subject tests are prime instructional time, professional d evelopment, the percent of teachers with advanced degrees, student teacher ratio, teacher attendance rate, the percent of Asian students, and the percent of students with another minority identity.
! )$ Table 2.12 Significant Parameter Estimates For Schools i n Which More than 50% of the Test Takers are Eligible for FRL ab Independent Variable Dependent Variable: % of students who met or exceeded state standards -------------------------------------------------------------------------------------------------------------------------------------------------English Math Science Social Studies Writing N=90 N=86 N=83 N=82 N=90 Expenditure on Instruction -0.499** ---Prime Instructi onal Time 1.567*** 1.754** 2.036*** -1.404 ** Teacher's Returning Rate -0.389** -0.556*** 0. 346** Percent of Bla ck Students -0.181* 0.295*** --Percent of Female Students 0.268* --0.379** -Percent of Students Eligible for FRL ---0.300* ---------------------------------------------------------------------------------------------------------------------------------------------------a. Note: Significance Levels: .10, ** .05, *** .01 ./! The variables that do not have significant estimates for any of the five subject tests are expenditure per student, teacher salary professional development, the percent of advanced degrees, student teacher ratio, teacher attendance rate, the percent of Asian students, and the percent of students with another minority identity.
! )% Chapter 5: Conclusion The purpose of this study i s to analyze the education production function for South Carolina to find the returns to education inputs, ultimately determining whether higher education inputs result in higher student achievement. T he results would seem to suggest education resources do not matter in this education production process across all five academic subjects. However this seems improbable. Rather, it is more likely that the results suggest that the resources are not being u sed effectively. Thus, structural changes are needed, as opposed to the technical changes, where technical changes are simply increasing school resources. The study 's results reflect Hanushek's conclusion that the relationships between education inputs an d level of achievement are weak and inconsistent ( "Assessing" 148). The fact that some inputs have statistically significant parameter estimates when analyzing some subject tests but not when analyzing other reflects the inconsistencies in previous literat ure, as well Math achievement is frequently the variable that is positively related to school inputs (Ram ; Clotfelter, Ladd, and Vigdor) In measuring education attainment through the percent of students per school that met or exceeded state assessment s tandards, it appear s that there is not enough evidence to support the idea that school inputs are directly related to student achievement I hypothesized that school inputs were favorably related to student achievement. However, there is not a direct relat ionship between school inputs and student achievement across the five subject tests studied: English Language Arts,
! )& Mathematics, Science, Social Studies, and Writing. In addition, the estimates expenditure per student and the percent of expenditure on inst ruction have a sign that is the opposite of the sign hypothesized. In considering the inconsistency and weakness of the relationships between education inputs and student achievement, it is important to consider the possibility of endogeneity problems. T here is "potential endogeneity of school resources, which could be correlated with the unobservable abilities throu gh their self sorting" (Checchi 97). The issue of endogeneity may be present if more inputs are invested in students with lower levels of ac hievement (98). Below, the specific findings of this study are discussed. In general, the results reflect the inconsistencies and un predictable nature of the relationship between school inputs and student achievement reported in the reviewed education p roduction function studies. Expenditure and Student Achievement The expenditure per student coefficient is negative an d statistically significant in M ath for the main analysis Expenditure per student is correlated with the percent of students that are eligible for FRL, as evidenced by the correlation coefficient of 0.30. T he negative relationship may illustrate that the funds going to improve the opportunity for under advantaged students are not being expended effectively enough, which would be measured by their ability to achieve as well as more advantaged students.
! )' The coefficient of expenditure that was spent on instruction is negative and st atistically significant in the M ath analysis for both the main analysis and for schools in which over 50% of t he test takers are eligible for F RL. This suggests that the expenditure on instruction is not used effectively. Teachers and Student Achievement The coefficient for the percent of teachers returning is positive and statistically significant for al l of the main analyses, except S cience. It is also positive and statistically significant for Math, Social Studies, and W riting in schools in which more than 50% of the students are eligible for free or reduced price lunch. The positive and statistically signif icant relationship could be related to a number of aspects. The return rate of teachers could illustrate their investment in the school and education process. Teachers who stay in one school over a span of time could gain more respect from the student body This would also allow teachers to get to know the students, and provide advice to other teachers as to how to work with specific students. In reviewing the corre lation coefficient for English Language A rts between the teacher return rate and percent of test takers eligible for FRL, it is 0.42352. This suggests that it is possible that teachers have a higher returning rate in schools with less under advantaged students. This form of self selection may influence the relationship between student achieveme nt and the percent of teachers who return from the previous year.
! )( The estimates for the percent of teachers returning are greater for Math, Social Studies, and Writing in schools in which more than 50% of the test takers are eligible for FRL in comparison to the main analysis. This suggests that a 1% increase in teachers returning yields greater returns for disadvantaged students, or that the marginal returns for the percent of teachers returning is greater for schools in which more than 50% of the student s are eligible for FRL. This result is similar to the results of the Coleman Report which finds that school and teacher inputs have a greater relationship with the achievement of minority students (Coleman et al. 22). Te acher's salary is also positively related student achievement in English L angu age Arts and M ath in the main analysis This may illustrate that teacher salary matches the quality of the teacher, which is an ideal purpose of using teacher salary as an input in the education production functi on. These results may also suggest that higher salary motivates teachers. The English Language A rts correlation coefficient for teacher salary and the percent of test takers eligible for FRL is 0.24511. This illustrates a negative relationship between the average teacher salary and the percent of students eligible for free or reduced lunch Thus, the results may also suggest that teachers with a higher salary work in classrooms with fewer disadvantaged students. Classroom Characteristics and Student Achie vement The majority of the classroom characteristic estimates were not statistically significant. However, the measure of prime instructional time is positive and statist ically significant for English Language Arts, M at h, Science, and W riting in schools i n which more than 50% of the test takers were eligible for FRL. This may
! )) suggest that the instruction time is important for the achievement of disadvantaged students. Student Body Demographics and Student Achievement In the main regression analysis, a n umber of student body demographic control variables are statistically significant. The percent of students eligible for FRL is negative and statistically significant for every subject tested in the main analysis This suggests that there may be barriers pr eventing economically disadvantaged students from receiving an education. The negative and statistically significant estimates for the percent of students who identify as black on all five subject tests reflect the persistent academic achievement gap in th e United States. The negative and statistically significant relationships for both black students and students who are eligible for FRL may illustrate the relationship between race and class in the United States. The Eng lish Language A rts correlation coeff icient for the percent of black students and the percent of students eligible for FRL is 0.73563 suggesting that these variables are positively related Certain racial minority groups, such as black students, make up a larger portion of schools that prima rily serve economically disadvan taged students (Kober and Usher 8). In the main regression analysis, the percentage of female students is positive and statist ically significant for English Language Arts, Social S tudies, and W riting. This reflects document ed female student achievement, in which females have higher achievement levels in reading and writing (Freeman 28)
! )* Policy Implications There are two main policies implications derived from the results of this study. One is that there should be greater focus on teacher behavior variables. Specifically, the results suggest that there should be greater focus on the teacher returning rate in order to improve the level of student achievement per school. However, this may not be important if the return rate o f teachers is related to the percent of students eligible for free or reduced price lunch. For example, the English Language Arts correlation coefficient for the percent of teachers returning and the percent of students eligible for FRL is 0.42352 sugges ting a negative relationship between the percent of teachers returning and the percent of students eligible for FRL. The relationship between the percent of teachers returning and student achievement may be influenced by the self selection of teachers. The second policy suggestion is to track the actual utilization of school inputs, rather than just the distribution of the resources "Dealing with the distribution of funding is attractive because it permits the active design of educational policies without getting into the details of how individual districts carry out their missio ns" (Hanushek, "School Resources" 44). Hanushek highlights the fact that, while personal benefits, externalities, and the costs of public education provide sufficient interest for e ducation policy, "student achievement seems unrelated to the standard measures of the resources going into schools" (43). However, this does not mean that school resources overall do not influence student achievement. A greater contribution to education re search may be to focus on how resources are being used, rather than just the distribution of resources. This may give a b etter account of how resources
! )+ relate to student achievement. Having a better understanding of how resources relate to student achievem ent will provide policy makers with some of the knowledge necessary to produce effective policy. Economists and policy makers should be concerned as to whether or not public funds are being expended effectively in order to increase future levels of human capital. Thus, programs should be evaluated to understand how public funds are being used. For example in "Evidence from Fifteen Schools in Austin, Texas," Richard Murnane and Frank Levy illustrate the problem with evaluating the use of public funds at an aggregate level by presenting conflicting evidence that was found by evaluating the use of public funds in individual school programs. For the schools in this study, conducted between 1989 and 1993, the school populations had a majority group of minority students and students from a lower economic class (93) Only two of the fifteen school s, Zavala and Ortega increased levels of achievement after receiving $300,000 every year. The two schools that increased their students' levels of achievement changed s ignificant aspects of the education process rather than just expending the increase in education funds without changing their education model. For example, all of the schools that received the increase in funds reduced the teacher student ratio (94). Howev er, the schools that increased their students' levels of achievement also changed the curriculum, invested in student services, and worked to increase parent participation (95). In analyzing the program of the two schools that increased levels of achieveme nt in comparison to the thirteen schools that continued to have low levels of achievement, the Texas study illustrates the importance of program structure to yield positive returns on education
! ), investment. Zavala and Ortega had positive returns to the inve stment of public funds in education by reforming their education system. Future Studies Future studies will take issues of endogeneity into account This can be done through utilizing a value added approach, which measures the contribution of inputs to a student's achievement (Checchi 98). Value added studies require a panel data set that contains a change in education inputs. A study tracking the achievements and backgrounds of individual students would be ideal. "While there is strong evidence tha t public schools do not act in line with the principle of profit maximization, it is not yet clear why this occurs" (Checchi 105). Future studies will also incorporate the disaggregated utilization and disaggregated level s of the education inputs. This wou ld assist in determining why certain resources are not producing expected results. A number of the inputs are human inputs, and that may be a reason that it is difficult to standardize the education production function. Variables such as teacher, peer, and student attitude may influence the relationship between student achievement and education inputs, and a disaggregated study may be able to capture the effects of more individualized human variables. While the majority of the variables lack statistical significance, and s ome estimates even carry a sign that is opposite than expected this does not necessarily mean education resources do not influence student achievement. However, it does mean that education policy and how the education production functio n is analyzed should be reconsidered. Money itself as well as other education inputs in this study,
! *! are not directly related to education achievement. As well, there is still a significant and negative relationship between the percent of students who are eligible for free or reduced price lunch and student achievement. There is a positive relationship in English Language Arts between expenditure per student and the percent of students eligible for FRL, as illustrated by a positive correlation coefficient ( 0.303). However, the consistent negative relationship between the percent of students eligible for FRL and student achievement may express simply that increasing resources for schools does not produce the necessary structural changes of the education syste m, and thus it is not enough to close the achievement gap. While, in part, achievement may be dependent on the distribution of resources, it may also be dependent on the way the resources are utilized.
! *$ Appendix A : Correlation Tables 01.23!4$!5672"89!:6;3<36;36=!16;!>3<36;36=!?1@"1.23!A B@@321="B6!01.23
! *% 01.23!4%!C1=93D1="E8!:6;3<36;36=!16;!>3<36;36=!?1@"1.23!AB@@321="B6!01.23
! *& Appendix B: Independent Variable Descriptive Statistics Table B1 Main Analysis Independent Variable Mean, Minimum, and Maximum Variable N Mean Minimum Maximum elaN_black_p elaN_asian_p elaN_other_p elaN_female_p elaN_sub_p mathN_black_p mathN_asian_ p mathN_other_p mathN_female_p mathN_sub_p sciN_black_p sciN_asian_p sciN_other_p sciN_female_p sciN_sub_p socN_black_p socN_asian_p socN_other_p socN_female_p socN_sub_p writN_black_p writN_asian_p writN_other_p writN_female_p writN_sub_p Y2012_t ExpendIn s Prime_time Salary_t Prof_dev PerAdvancedDegrees StudentTeacherRatio TeacherAttend TeachersReturning 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 299 285 285 276 294 296 296 286 283 278 41.896 0.903 7.0 62 48.547 60.298 41.880 0.921 6.659 48.548 60.296 41.566 0.950 7.089 49.046 59.952 41.938 0.890 6.958 47.932 60.434 42.243 0.888 6.995 48.342 60.488 7.824 62.647 89.658 45.819 11.018 60.691 21.956 95.207 84.360 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3.745 42.500 23.300 20.000 0.300 7.700 3.700 85.100 48.900 100.000 6.340 39.444 100.000 100.000 100.000 6.322 39.227 100.000 100.000 100.000 6.522 40.426 100.000 100.000 100.000 11.765 39.080 100.000 100.000 100.000 6.268 40.909 75.000 100.000 45.75 9 92.000 99.400 56.309 61.400 100.000 38.300 100.000 96.100
! *' Table B2 Schools in which more than 50% of English Language Arts Test Takers are Eligible for FRL Independent Variables Mean, Minimum, and Maximum Variable N Mean Minimum Maximum elaN_bl ack_p elaN_asian_p elaN_other_p elaN_female_p elaN_sub_p Y2012_t ExpendIns Prime_time Salary_t Prof_dev PerAdvancedDegrees StudentTeacherRatio TeacherAttend TeachersReturning 150 150 150 150 150 139 139 140 146 148 147 143 141 138 60.190 0.508 6.952 48.023 77.803 8.555 61.180 88.763 44.998 11.418 59.609 21.179 95.178 81.750 8.182 0 0 0 60.352 3.745 42.500 23.300 26.000 0.300 26.700 3.900 85.100 48.900 100.000 5.555 39.444 75.000 100.000 21.939 75.000 99.400 56.309 61.400 100.000 38.300 100.000 95.000 T able B3 Schools in which more than 50% of Math Test Takers are Eligible for FRL Independent Variables Mean, Minimum, and Maximum Variable N Mean Minimum Maximum mathN_black_p mathN_asian_p mathN_other_p mathN_female_p mathN_sub_p Y2012_t ExpendIns Prime _time Salary_t Prof_dev PerAdvancedDegrees StudentTeacherRatio TeacherAttend TeachersReturning 149 149 149 149 149 138 138 139 145 147 146 142 140 137 60.473 0.522 6.365 48.047 77.918 8.566 61.194 88.753 44.964 11.428 59.560 21.151 95.180 81.655 8.182 0 0 0 60.352 3.745 42.500 23.300 26.000 0.300 26.700 3.900 85.100 48.900 100.000 5.556 39.227 75.000 100.000 21.939 75.000 99.400 56.309 61.400 100.000 38.300 100.000 95.00
! *( Table B4 Schools in which more than 50% of Science Test Takers are Eligible for FRL Independent Variables Mean, Minimum, and Maximum Variable N Mean Minimum Maximum sciN_black_p sciN_asian_p sciN_other_p sciN_female_p sciN_sub_p Y2012_t ExpendIns Prime_time Salary_t Prof_dev PerAdvancedDegrees StudentTeacherRatio TeacherAttend Teachers Returning 149 149 149 149 149 138 138 140 146 148 147 143 141 138 59.794 0.587 6.789 47.940 78.256 8.833 61.081 88.567 44.985 11.295 59.441 21.150 95.086 81.608 0 0 0 0 60.606 3.745 42.500 23.300 26.000 0.300 26.700 3.900 85.100 48.900 100.000 5.426 40 .426 100.000 100.000 45.759 75.000 98.300 56.309 61.400 100.000 38.300 100.000 95.000 Table B5 Schools in which more than 50% of Social Studies Test Takers are Eligible for FRL Independent Variables Mean, Minimum, and Maximum Variable N Mean Minimum Maximum socN_black_p socN_asian_p socN_other_p socN_female_p socN_sub_p Y2012_t ExpendIns Prime_time Salary_t Prof_dev PerAdvancedDegrees StudentTeacherRatio TeacherAttend TeachersReturning 150 150 150 150 150 141 141 141 146 148 147 141 141 138 59.129 0.412 6.687 47.691 78.239 8.503 61.115 88.568 44.987 11.478 59.628 21.142 95.091 81.764 4.706 0 0 0 60.526 3.745 42.500 23.300 26.000 0.300 26.700 3.900 85.100 48.900 100.000 5.714 39.080 75.000 100.000 21.939 75.000 99.400 56.309 61.400 100.000 38.300 1 00.000 95.000
! *) Table B6 Schools in which more than 50% of Writing Test Takers are Eligible for FRL Independent Variables Mean, Minimum, and Maximum Variable N Mean Minimum Maximum writN_black_p writN_asian_p writN_other_p writN_female_p writN_sub_p Y 2012_t ExpendIns Prime_time Salary_t Prof_dev PerAdvancedDegrees StudentTeacherRatio TeacherAttend TeachersReturning 149 149 149 149 149 138 138 139 145 147 146 142 140 137 60.787 0.461 6.872 47.864 78.136 8.560 61.195 88.736 44.961 11.496 59.588 21.124 9 5.184 81.608 8.190 0 0 0 60.645 3.745 42.5000 23.300 26.000 0.300 26.700 3.900 85.100 48.900 100.000 5.556 40.909 75.000 100.000 21.939 75.000 99.400 56.309 61.400 100.000 38.300 100.000 95.000
! ** Appendix C : Diagnostic Tests 01.23!A $!F9"=3!038=!G38 H2=8 CB;32 < I #12H3 CB;32!$J!521
! *+ M"7H@3!A% CB;32!% C1=9 O3=3@B8P3;18="E"=Q M"7H@3! A& CB;32!&! KE"36E3! O3=3@B8P3;18="E"=Q ! Residual -50 -40 -30 -20 -10 0 10 20 30 Predicted Value 30 40 50 60 70 80 90 100 Residual -40 -30 -20 -10 0 10 20 30 Predicted Value 50 55 60 65 70 75 80 85 90 95 100
! *, M"7H@3! A' CB;32!'! KBE"12!K=H;"38! O3=3@B8P3;18="E"=Q M"7H@3!A( CB;32!( F@"="67 O3=3@B8P3;18="E"=Q Residual -40 -30 -20 -10 0 10 20 30 40 Predicted Value 30 40 50 60 70 80 90 100 Residual -40 -30 -20 -10 0 10 20 30 Predicted Value 50 55 60 65 70 75 80 85 90 95 100
! +! 01.23!A%!CB;32!$!5672"89!N167H173!4@=8!CH2="EB22"631@"=Q ?1@"1.23 ?"R 5S<36;"=H@3!T 3@!K=H;36= %/$&)*$ T3@E36=!BR!3S<36;"=H@38!H83;!RB@!"68=@HE="B6 $/)'*)% T@"D3!"68=@HE="B612!="D3 $/&$&)) 031E93@!8121@Q $/,)''+ T@BR388"B612!;3#32B
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! +% 01.23!A)!CB;3 2!(!F@"=
! +& Works Cited Archibald, Sarah. "Narrowing in on Educational Re sources That Do Affect Student Achievement." Peabody Journal of Education 81.4 (2006) 23 42. Baddeley, M. C. and D.V. Barrowclough. Running Regressions. A Practical Guide to Quantitative Research in Economics, Finance and Development Studies. New York: Cam bridge University Press. 2009. Baker, Bruce, David Sciarra, and Danielle Farrie. Is School Funding Fair? A National Report Card Newark: Education Law Center, 2010. Bosworth, Ryan. "Class Size, Class Composition, and the Distribution of Student Achieveme nt." Eduation Economics (2011) 1 25. Bowles, Samuel. "Towards an Educational Production Function." Education, Income, and Human Capital. Ed. W. Lee Hansen. UMI, 1970. 9 70. Bowles, Samuel and Herbert Gintis. Schooling in Capitalist America. 2011 ed. Chica go: Haymarket Books, 2011. Bowles, Samuel and Henry Levin. "The Determinants of Scholastic Achievement an Appraisal of some Recent Evidence." The Journal of Human Resources 3.1 (1968): 3 24. Bowles, Samuel and Henry Levin. "More on Multicollinearity and the Effectiveness of Schools." The Journal of Human Resources 3.3 (1968): 393. Burtless, Gary. "Introduction and Summary." Does Money Matter? The Effect of School Resources on Student Achievement and Adult Success Ed. Gary Burtless. Washington D.C.: Bro okings Institute Press, 1996. 1 41. Checchi, Daniele. The Economics of Education: Human Capital, Family Background, and Inequality New York: Cambridge University Press, 2006. Chudowsky, Naomi, and Victor Chudowsky. State Test Score Trends through 2007 0 8, Part 5 : Are there Differences in Achievement between Boys and Girls Ed. Nancy Kober. Washington, D.C.: Center on Education Policy, 2010. Chudowsky, Naomi, and Victor Chudowsky. State Test Score Trends through 2008 09, Part 3: Student Achievement at 8t h Grade Ed. Nancy Kober. Washington, D.C.: Center on Education Policy, 2011.
! +' Clotfelter, Charles; Ladd, Helen; and Jacob Vigdor. "Teaher Credentials and Student Achievement: Longitudinal Analysis with Student Fixed Effects." Economics of Education Revie w 26 (2007) 673 682. Chetty, Raj; Friedman, John and Jonah Rockoff. "The Long Term Impacts of Teachers: Teacher Value Added and Student Outcomes in Adulthood." 2011. NBER Working Paper No. 17699. Coates, Dennis. "Education Production Functions Using Inst ructional Time as an Input." Education Economics 11.3 (2003) 273 292. Coleman, James, et al. Equality of Educational Opportunity. Washington, D.C.: U.S. Government Printing Office. 1996. Dixon, Mark. Public Education and Finances: 2010 G10 ASPEF Vol. 201 2: U.S. Government Printing Office. Freeman, Catherine E. Trends in Educational Equity of Girls & Women: 2004 NCES 2005 016 Vol. Washington, DC: U.S. Government Printing Office, 2004. "FY10 11 Finance FAQs." South Carolina State Department of Education South Carolina State Government.
! +( O31@6V!AQ6=9"1/!WG3J!>1=1!XH38="B6/Y!C388173!=B!1H=9B@/!%-!ZB#/!%-$%/!5 I D1"2/ Howe, Harold. Letter of Transmittal. Equality of Educational Opportunity. By Coleman, James, et al., Washington, D.C.: U.S. Gove rnment Printing Office. 1996. iii iv. Huffman, Douglas; Thomas, Kelli; and Frances Lawrenz. "Relationship Between Professional Development, Teachers' Instructional Practices, and the Achievement of Students in Science and Mathematics." School Science and Mathematics 103.8 (2003) 378 387. Jennings, Jack. Reflections on a Half Century of School Reform: Why have we Fallen Short and Where do we Go from here? Ed. Nancy Kober. Washington, D.C.: Center on Education Policy, 2012. Jinette, Mellanie. 2011 2012 Funding Manual South Carolina Department of Education Office of Finance. Kober, Nancy, and Alexandra Usher. A Public Education Primer: Basic (and Sometimes Surprising) Facts about the U.S. Educational System Washington, D.C.: Center on Education Policy, 2012. Kober, Nancy. A Call to Action to Raise Achievement for African American Students Washington, D.C.: Center on Education Policy, 2010. Lareau, Annette. Unequal Childhoods: Class, Race, and Family Life. Berkeley: University of California Press, 2003 Levy, Frank and Richard J. Murnane. "Evidence from Fifteen Schools in Austin, Texas." Does Money Matter? The Effect of School Resources on Student Achievement and Adult Success Ed. Gary Burtless. Washington D.C.: Brookings Institute Press, 1996. 93 96. Marlow, M. L. "Spending, School Structure, and Public Education Quality. Evidence from California." Economics of education review 19.1 (2000): 89. "Mathematics 2011 State Snapshot Report." National Report Card Institute of Education Sciences.
! +) "North America: United States." The World Factbook Central Intelligence Agency. Web. 17 Apr 2013.
! +* South Carolina State Government. Department of Education. State Assessments. 2011.